relevant reading:
http://en.wikipedia.org/wiki/Monarchy_of_Australia
Think of her as being simultaneous monarch of several countries that are now independent of each other.
http://en.wikipedia.org/wiki/Australia_Act_1986
http://www.theaustralian.com.au/opinion/we-only-became-indep...
"While the public was not aware of the true position, the politicians were. Political leaders saw the price paid for being colonial dependencies of the British crown and it was too high. After years of negotiations the constitutional links between Australia and Britain were finally broken , not by a referendum but by legislation passed by the state, commonwealth and British parliaments. On March 3, 1986, these acts, the Australia Acts, came into force. They state that the British government is no longer responsible for the government of any state and that the Westminster parliament can no longer legislate for Australia. Most important, they transferred into Australian hands full control of all Australia's constitutional documents. So March 3, 1986, is the day Australia achieved complete independence from Britain. Happy Australian Independence Day."
The Queen of England is also still nominally head of state of Canada. Not that this has much effect in practice.