Question: My Australian friend says yes. I'm not so sure, considering the monarchy collects no taxes from England, much less a country in the commonwealth. What's the verdict? Can she say "you're fired" and Tony Abbot is out?

Answer: 
*Theoretically*, yes.

The prime minister is appointed by the governor-general, who is the representative of the Australian monarch (currently Queen Elizabeth II). The queen could instruct her representative to appoint a new prime minister at any time. (If the governor-general refused, the queen could appoint a new governor-general.)

*In practice*, however, the governor-general *usually* only appoints a new prime minister as advised by Parliament or a resigning prime minister.

(In a rare exception to this practice, in 1975 the governor-general dismissed a prime minister whose party held a majority in the House. ([Wikipedia](http://en.wikipedia.org/wiki/1975_Australian_constitutional_crisis)))

Also in practice, the monarch usually only appoints a governor-general that has been nominated by the prime minister.

It's important to remember that Elizabeth doesn't have these powers as queen of England, but as **queen of Australia**. Legally, Australia is a monarchy, with its own royal family. It happens to be that this royal family resides in England, and that the queen of Australia is *also* queen of several other countries, but only for historical reasons.
1. The Queen Cannot sack the Prime Minister of Australia.
2. In 1975, (I was there) the Governor General did NOT sack the Prime Minister, he has no power to sack the Prime Minister.
3. What can happen is this. If the Parliament cannot get legislature through parliament, due to blockage of the other side. Again and again. And 'supply is blocked'... i.e. money to be allocated, Parliament comes to a standstill. The Prime Minister can approach the Governor General and request a 'Double Dissolution' Both the Upper and Lower houses are disbanded, and a new election for both upper and lower houses are called for. This is what occurred in 1975. Whitlam couldn't get legislature through. There was an election, and Malcolm Fraser and Liberals were voted in.