Also a few other countries, but word is some of them speak French, and that hasn't been cool for a very long time indeed.
The head of state is of course the Governor General, who is the Queen of Australia's representative in Australia. Their role is to sign legislation into law, dissolve parliament, and appoint prime ministers, which they are required to do by law when (and only if) the legislation, dissolution, or appointment was lawfully passed by a majority of the House of Representatives (and also the Senate for legislation). They also cut those ribbons at various ceremonies.
The Prime Minister appoints a cabinet who must all be from the House, which is the natural and right-minded place for people to have their executive be from. They also chose for appointment various other people, including the new Governor General.
As long as it's the Queen of Australia, you're not in any trouble at all. Don't be shitting out the future Queen of Denmark or something, just because she's an Australian.I'm so British I shit the Queen.