I've got a few American readers so we'll start by clearing up the confusion: she is NOT the Queen of Australia, she's the Queen of England and as such has dominion over us and other Commonwealth nations.
Charlie (Prince Charles) is her son and next in line for the crown then come his and Diana's boys, Princes Wills and Harry. Poor Harry looks more like his dad every day but, thank Christ, Wills looks like his mum.
Governors and Governors General
Each state has a Governor and the whole of Australia has a Governor General. They have the power to dismiss our Premiers and Prime Ministers. In 1975 the most notorious of our Governors General, Kerr ("Kerr by name cur by nature") dismissed Whitlam.
Our current Governor General is Major General Michael Jeffery and NSW's current Governor is Professor Marie Bashir.
Premiers and Prime Ministers
Premiers head each state and Prime Ministers head the country. Yes, this means we've got two heads of each state (Governor & Premier) and two heads of Australia (Governor General & Prime Minister). Technically this means we're ruled by the English Crown but, since 1975, the Queen has made it known we control our own destiny.
Our current PM is John Weasel Howard (pictured).
A few of our better-known PMs:
Edmund Barton, our first one. 1st of March 1901 Parliament was opened by the Duke of York (later crowned George V). Before Federation each state was a British colony and federation was agreed on by a vote and we've never fought a war against England. Australian national identity kicked in 1915 in Gallipoli.
Harold Holt, the one we lost. And yes, we really did name a swimming pool after him.
Gough Whitlam, the one who got the sack.
Bob Hawke, the PM who cried and got pissed on TV when we won the America's Cup.
Paul Keating, the PM we had to have.
Democrats. NOT like the American democrats. Too rational to be real politicians. They've suffered several implosions recently but are still going strong.
Get some fucking policies already! And put The Beazer on a diet. The bastard looks like he'll be carried out of parliment in an ambulance one day. This party suffers implosions almost daily.
Liberal my arse. Shows you what bullshit there is in politics. These bastards are conservative through and through. They just fucked us over with the new industrial reform crap. Talk about a great leap backwards. Their leader is our current PM, John Howard, a closet comb-over and sulky bastard.
Conservative rural party. Half the time these buggers form a coalition with the Libs to keep Labor out of the big chair. This leads to regular implosions and the Nats threatening to take their party and go home.
Still confused? Here's one someone else made earlier.