The National Archives of Australia, which houses government records, was initially part of the National Library, but became and independent agency in 1961.  NAA's main repository is in Mitchell in the north of Canberra (Gungahlin district) and there are repositories in each state and the Northern Territory.

Some of Australia's founding documents can be viewed in "Voices / Dhuniai: Federation, democracy and the Constitution," one of two permanent exhibitions.  It took about almost a decade to develop the Constitution.  An Australasian Federation Conference was held in Melbourne on 6-14 February 1890, and the National Australasian Convention took place in Sydney on 2 March-9 April 1891.  However, a recession and other matters intervened, and did not discussions and debate did resume until the Australasian Federation Convention met in three sessions in 1897-98. 
Edmund Barton's notebook from the Australasian Federal Convention in 1897 shows revisions to the 1891 draft and several doodles.  Barton served as convention leader and chairman of the constitutional committee (>).
An example of a petition.

The Commonwealth of Australia Constitution Act, was drafted at conventions in the 1890s (>), and approved in referendums (>).  Edmund Barton led a delegation to Britain, and after extensive lobbying the British Parliament adopted the Act and on 9 July 1900 Queen Victoria gave her Royal Assent.  The Act finally came into effect on 1 January 1901.  The document weighs in at 25 pages.  The first two pages describe the creation of the Commonwealth and the remaining pages are the Australian Constitution, consisting of eight chapters. 
Queen Victoria's Royal Assent:

Victoria by the Grace of God of the United Kingdom of Great Britain and Ireland Queen Defender of the Faith To Our right trusty and right well beloved The Lords Spiritual and Temporal and to Our trusty and well beloved The Knights Citizens and Burgesses of the House of Commons in this present Parliament assembled Greeting:

Whereas in Our said Parliament an Act the short title whereof is Commonwealth of Australia Constitution Act, 1900, hath been agreed and accorded on by you Our loving Subjects the Lords Spiritual and Temporal and the Commons in this Our present Parliament assembled and endorsed by you as hath been accustomed And albeit the said Act by you Our said Subjects the Lords and Commons in this Our present Parliament assembled is fully agreed and consented unto yet nevertheless the same is not of force and effect in the law without Our Royal Assent given and put to the said Act And forasmuch as for divers causes and considerations We cannot conveniently at this time be present in Our Royal Person in the Higher House of Our said Parliament being the accustomed place for giving Our Royal Assent to such Acts as have been agreed upon by you Our said subjects the Lords and Commons We have therefore caused these Our Letters Patent to be made and have signed the same and by the same Do give and put Our Royal Assent to the said Act and to all articles clauses and provisions therein contained and have fully agreed and assented to the said Act Willing that the said Act and every article clause sentence and provision therein contained from henceforth shall be of the same strength force and effect as if We had been personally present in the said Higher House and had openly and publicly in the presence of you all assented to the same And We do by these presents declare and notify the same Our Royal Assent as well to you the Lords Spiritual and Temporal and Commons aforesaid as to all others whom it may concern Commanding also by these presents Our most dear Cousin and Councillor Hardinge Stanley Earl of Halsbury Our Chancellor of that part of Our United Kingdom of Great Britain and Ireland called Great Britain to seal these Our Letters Patent with Our Great Seal of Our United Kingdom of Great Britain and Ireland And also commanding Our most dear and entirely beloved Sons and most faithful Councillors Albert Edward Prince of Wales, Arthur William Patrick Albert Duke of Connaught and Strathearn, Our most dear Grandson and most faithful Councillor George Frederick Ernest Albert Duke of York, Our most dear Cousin and faithful Councillor George William Frederick Charles Duke of Cambridge, The Most Reverend Father in God and Our faithful Councillor Frederick Archbishop of Canterbury Primate of all England and Metropolitan, Our most dear Cousin and Councillor Hardinge Stanley Earl of Halsbury Chancellor of that part of Our United Kingdom of Great Britain and Ireland called Great Britain, The Most Reverend Father in God and Our faithful Councillor William Dalrymple Archbishop of York primate of England and Metropolitan, Our most dear Cousins and Councillors Spencer Compton Duke of Devonshire President of Our Council, Richard Assheton Viscount Cross Keeper of Our Privy Seal, Sidney Earl of Pembroke and Montgomery Steward of Our Household, John Adrian Louis Earl of Hopetoun Chamberlain of Our Household, Algernon Hawkins Thomond Earl of Kintore and other Lords of Our Privy Council or any three or more of them to declare and notify this Our Royal Assent in Our absence in the said Higher House in the presence of you the said Lords and Commons of Our Parliament there to be assembled for that purpose and the Clerk of Our Parliaments to endorse the said Act with such terms and words in Our name as is requisite for the same and also to enrol these Our Letters Patent and the said Act in manner accustomed and these Our Letters Patent shall be to every of them a sufficient Warrant in that behalf And finally We do declare and will that after this Our Royal Assent given and passed by these presents and declared and notified as is aforesaid then and immediately the said Act shall be taken accepted and admitted a good sufficient and perfect Act of Parliament and Law to all intents constructions and purposes and to be put in due execution accordingly the continuance or dissolution of this Our Parliament or any other use custom thing or things to the contrary thereof notwithstanding In witness whereof We have caused these Our Letters to be made patent Witness Our self at Westminster the ninth day of July in the sixty fourth year of Our reign. __________________________________

By the Queen Herself
Signed with Her own Hand
Muir Mackenzie

Dated 9th July 1900
Royal Assent
of
Her Majesty the Queen
to
Commonwealth of Australia Constitution Act 1900
source: www.foundingdocs.gov.au
Page 2 of the Letters Patent, signed 29 October 1900, which established that the Queen's powers are exercised by a Governor-General:

VICTORIA by the Grace of God of the United Kingdom of Great Britain and Ireland, Queen, Defender of the Faith, Empress of India To all to whom these Presents shall come Greeting.
Whereas, by an Act of Parliament passed on the ninth day of July One thousand nine hundred, in the Sixty fourth year of Our reign, intiluled “An Act to constitute the Commonwealth of Australia,” it is enacted that “it shall be lawful for the Queen,” with the advice of the Privy Council, to declare by Proclamation that, on and after a day therein appointed, not being later than one year after this passing of this Act, the people of New South Wales, Victoria, South Australia, Queensland, and Tasmania, and also, if Her Majesty is satisfied that the people of Western Australia have agreed thereto, of Western Australia, shall be united in a Federal Commonwealth under the name of the Commonwealth of Australia. But the Queen may, at any time after Proclamation, appoint a Governor General for the Commonwealth:”
And whereas We did on the seventeenth day of September One thousand nine hundred, by and with the advice of Our Privy Council declare by proclamation that, on and after the first day of January One thousand nine hundred and one, the people of New South Wales, Victoria, South Australia, Queensland, and Tasmania and also Western Australia, should be united in a Federal Commonwealth under the name of the Commonwealth of Australia: And whereas by the said recited Act certain powers, functions, and authorities were declared to be vested in the Governor General: And whereas We are desirous of making effectual and permanent provision for the office of Governor General and Commander in chief in and over Our said Commonwealth of Australia, without making new Letters Patent on each demise of the said office Now know ye that We have thought fit to constitute, order, and declare, and do by these presents constitute order, and declare, that there shall be a Governor General and Commander in Chief (hereinafter called the Governor General) in and over Our Commonwealth of Australia (hereinafter called Our said Commonwealth), and that the person who shall fill the said office of Governor General shall be from time to time appointed by Commission under Our Sign Manual and Signet. And we do hereby authorize and command Our said Governor General to do and execute, in due manner, all things that shall belong to his said command, and to the trust We have reposed in him, according to the several powers and authorities granted or appointed him by virtue of “The Commonwealth of Australia Constitution Act, 1900,” and of these present Letters Patent and of such Commission as may be issued to him under Our Sign Manual and Signet, and according to such Instructions as may from time to time be given to him under Our Sign Manual and Signet, or by Our Order in Our Privy Council, or by Us through one of Our Principal Secretaries of State, and to such laws as shall hereafter be in force in Our said Commonwealth.
II. There shall be a Great Seal of and for Our said Commonwealth which Our said Governor General shall keep and use for sealing all things whatsoever that shall pass the said Great Seal. Provided that until a Great Seal shall be provided the Private Seal of Our said Governor General may be used as the Great Seal of the Commonwealth of Australia.
III. The Governor General may constitute and appoint, in Our name and on Our behalf, all such Judges, Commissioners, Justices of the Peace, and other necessary officers and Ministers of Our said Commonwealth, as may be lawfully constituted or appointed by Us.
IV. The Governor General, so far as We Ourselves lawfully may, upon sufficient cause to him appearing, may remove from his office, or suspend from the exercise of the same, any person exercising any office of Our said Commonwealth, under or by virtue of any ---- Commission or Warrant granted, or which may be granted, by Us in Our name or under Our authority.

[PAGE ONE ENDS HERE]

V. The Governor General may on Our behalf exercise all powers under the Commonwealth of Australia Constitution Act, 1900, or otherwise in respect of the summoning, proroguing, or dissolving the Parliament of Our said Commonwealth.
VI. And whereas by “The Commonwealth of Australia Constitution Act 1900,” it is amongst other things enacted, that we may authorise the Governor General to appoint any person or persons, jointly or severally, to be his Deputy or Deputies within any part of Our Commonwealth, and in that capacity to exercise, during the pleasure of the Governor General such powers, and functions of the said Governor General as he thinks fit to assign to such Deputy or Deputies, subject to any limitations expressed or directions given by Us: Now We do hereby authorise and empower Our said Governor General subject to such limitations and directions as aforesaid, to appoint any person or persons, jointly or severally, to be his Deputy or Deputies within any part of Our said Commonwealth of Australia, and in that capacity to exercise, during his pleasure, such of his powers and functions, as he may deem it necessary or expedient to assign to him or them: Provided always, that the appointment of such a Deputy or Deputies shall not affect the exercise by the Governor General himself of any power or function.
VII. And We do hereby declare Our pleasure to be that, in the event of the death, incapacity, removal, or absence of Our said Governor General out of Our said Commonwealth, all and every the powers and authorities herein granted to him shall until Our further pleasure is signified therein, be vested in such person as may be appointed by Us under Our Sign Manual and Signet to be Our Lieutenant Governor of Our said Commonwealth: or if there shall be no such Lieutenant Governor in Our said Commonwealth, then in such person or persons as may be appointed by Us under Our Sign Manual and Signet to administer the Government of the same. No such powers or authorities shall vest in such Lieutenant Governor, or such other person or persons, until he or they shall have taken the oaths appointed to be taken by the Governor General of Our said Commonwealth, and in the manner provided by the Instructions accompanying these Our Letters Patent.
VIII. And We do hereby require and command all Our Officers and Ministers, Civil and Military, and all other the inhabitants of Our said Commonwealth to be obedient, aiding, and assisting unto Our said Governor General, or, in the event of his death, incapacity, or absence, to such person or persons as may, from time to time, under the provisions of these Our Letters Patent, administer the Government of Our said Commonwealth.
IX. And We do hereby reserve to Ourselves Our heirs and successors, full power and authority from time to time to revoke, alter, or amend these Our Letters Patent as to Us or them shall seem meet.
X. And We do further direct and enjoin that these Our Letters Patent shall be read and proclaimed at such place or places as Our said Governor General shall think fit within Our said Commonwealth of Australia.
In witness whereof We have caused these Our Letters to be made Patent Witness Ourself at Westminster the twenty ninth day of October in the sixty fourth year of Our reign.

By Warrant under the Queen’s Sign Manual
Muir Mackenzie
source: www.foundingdocs.gov.au
Museum of Australian Democracy in conjunction with the NAA.  "Documenting a Democracy."
Parliament of Australia.  "Constitutional Conventions."
Australian Electoral Commission.  "Fact Sheet 1 THE REFERENDUMS 1898-1900."
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Temporary Exhibition "Camel trains to steel wheels: life on the Trans-Australian Railway."
The Trans-Australian Railway, completed in 1917, linked Port Augusta in South Australia and Kalgoorlie in Western Australia, a distance of 1,693 km (1,052 miles).