Thanks for your question!
Gough Whitlam is the only Prime Minister to have been dismissed or fired in our history.
On the 11th November 1975 using the ‘Reserve Powers’ available to him in the Australian Constitution, the Governor-General, Sir John Kerr, terminated Mr Whitlam’s commission as Prime Minister.
You can read more about these events here.
Technically a Governor-General could fire a Prime Minister again however it would be a controversial decision.