I came across a tweet saying that there should be an Australian on the five dollar note, rather than Elizabeth II.
Legally speaking, is Elizabeth II Australian? Wikipedia mentions that she's Queen of Australia, but is she also an Australian, either as a citizen, permanent resident or via other legal rights?
The Queen doesn't need legal rights, she is the law!
As per Dale M's answer, Her Majesty doesn't meet the requirements to be a citizen of Australia under the Citizenship Act, nor has she ever been granted that status.
Someone else will need to fill in the legal reasons as to whether or not a law like the Migration Act could be enforced against Her Majesty personally. I suspect there is an argument in there about the Crown generally not being bound by statutes. In practice, I can't imagine anybody at the Department of Immigration trying to turn Her Majesty back at the border (although this would be an interesting step towards a republic...).
In any case the Royal Family and members of its entourage have the special status of not needing a visa when they visit Australia: Migration Regulations 1994, reg 2.40.
Queen Elizabeth II is not a citizen of Australia, she is the Sovereign of it. The preamble of the Commonwealth of Australia Constitution Act also refers to enactment by the Queen, and thus Her Majesty transcends the personal-instutional level.
I would still include her, as Queen of Australia, in the "Australian" category, yes.
Queen Elizabeth II was born in London to British parents who were not permanent residents of Australia. She does not meet any criteria under the Citizenship Act for being or applying for Australian citizenship.
