Bilbo, I may be incorrect, but permit me to reference the relevant document:

The Constitution of Australia defines the Parliament as "the Queen, a Senate, and a House of Representatives" and vests the Federal legislative (law-making) power in the Parliament (section 1, Constitution).

The executive power (the governing and administrative power) of the Commonwealth of Australia is vested in the Queen (section 61, Constitution).

The Queen has the power to disallow any law within one year of it being made even after the Governor-General has given his assent (section 59, Constitution).

The Governor-General only holds office "during the Queen's pleasure" which means that the he can be dismissed by the Queen at any time (section 2, Constitution).

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Eudaimonia