The Australian Constitution is a (now repealed) law of the defunct state of The United Kingdom of Great Britain and Ireland (known at the time as the British Empire) passed in the British parliament in 1900. The law gives orders and legal structure to a Federation of the various Colonies of Australia (namely: Queensland, New South Wales, South Australia, Victoria, Western Australia, the Northern Territory, and Tasmania) thereafter to be known as States under a single Federated unit to be known as the Commonwealth of Australia.
Nature of Constitution
The Australian constitution, being itself a law of Britain, could not and was never intended to create a sovereign nation. Rather, the purpose was to make governing the British colonies simpler for the Crown. Australia would, after federation, have a single Governor General to run political affairs at the highest level in the continent, as well as the separate Governors General in the States and Territories of the Federation.
It is often mistakenly held that the Constitution of Australia created the Nation of Australia. However Australia was only granted Sovereignty by the British Government at the end of World War II (indeed, returning Soldiers did so on British Passports).
Issues in Sovereignty
Upon being granted Sovereignty by the British Empire (which itself was winding up after the second World War), Australian politicians struggled to put in place a sovereign constitution as a legal foundation for the Australian body politic and statute law. However this was repeatedly unsuccessful and the issue fell out of political favour over time. The Federal Government and States and Territories of Australia continued to operate under the existing legal structure -- that of a British Colony. Some argue that this makes the Government of Australia an occupation government, or an illegal defacto government, the people being effectively denied the Right to Self Determination.