Monarchy of Australia
The title Queen of Australia has existed since 1973, when the Parliament of Australia passed the Royal Style and Titles Act (1973). This act repealed sections of the Royal Style and Titles Act (1953), which had been passed at the time of Queen Elizabeth II's accession to the Throne.
In the 1953 Act, Elizabeth's Australian style and titles were specified to be:
Elizabeth the Second, by the Grace of God of the United Kingdom, Australia and Her other Realms and Territories Queen, head of the Commonwealth, Defender of the Faith.
Under the 1973 Act her Australian style and titles became:
Elizabeth the Second, by the Grace of God Queen of Australia and Her other Realms and Territories, Head of the Commonwealth.
(It should be noted that "the Commonwealth" in this context is not the Commonwealth of Australia, but the Commonwealth of Nations, of which Australia is a member and the Queen is the Head.)
It will be noted that the title "Defender of the Faith" was deleted by this Act from the Queen's Australian style and titles. In the United Kingdom the Church of England is a state church, and the Queen is its "Supreme Governor." Australia has no state church, and neither the Queen nor the Governor-General have any official connection with the Anglican Church of Australia.
It is sometimes asserted that the 1973 Act establishes Australia as a monarchy completely separate from the monarchy of the United Kingdom, linked only by the fact that they happen to have the same monarch. This is not entirely true. When Elizabeth II dies or abdicates, for example, her successor as King or Queen of Australia will be determined according to the Act of Settlement of 1701, an act of the Parliament of the United Kingdom.
This Act provides that only Protestant descendants of Sophia, Electress of Hanover, who have not, furthermore, married a Catholic, can succeed to the Throne. This Act is on the face of it in conflict with Australian law preventing discrimination on grounds of religion, but this issue has never been tested.
Further, the Queen is only "Queen of Australia" when she is either present in Australia or (occasionally) when she performs certain ceremonies relevant to Australia (such as conferring Australian honours) in the United Kingdom. When she travels outside the United Kingdom, other than to Australia, she always travels as Queen of the United Kingdom.