The Australian constitutional system combines stability with flexibility unlike, say, the American republic. In the United States president can only be removed after a trial in the Senate whene he is found guilty of criminal conduct. Mere incompetence is not enough.

Remember too the President is the government, not the cabinet who are only advisory.

Unlike an American president, our prime minister is untenured and at all times dependent on the confidence of the lower house. This allows for one of the jewels of our system, that it allows an easy and peaceful transfer of political power. A leading example of this difference between the American system and Westminster came after the failed Bay of Pigs invasion of Cuba in 1961.
 

President Kennedy, who agreed he was responsible for the failed intervention, told the CIA deputy head:

 “If this were the UK, you as the civil servant would continue and I would resign. But it’s not. In the United States, I continue and you resign.”

If a Prime Minister loses the support of his party, the normal practice is to assume he has lost the confidence of the House and should resign.

If Mr. Rudd loses the vote in caucus, he could still ask the Governor-General  for a dissolution or double dissolution. Her Excellency would be entitled to ask him to first test whether the House has confidence in him.

In 1987, the Premier of Queensland, Sir Joh Bjelke-Petersen, advised the Governor, Sir Walter Campbell that he wanted to resign and to form a new government. Aware that the Premier had lost the confidence of his own Cabinet, the Governor pointed out to him that if he did resign he might not necessarily be recommissioned as Premier. Thus advised, Sir Joh did not submit his resignation. Soon afterwards he had to resign on losing the leadership of his party. The Governor then commissioned the National Party’s new leader, Mr Mike Ahearn, as Premier.

Our constitutional system works, and works superbly.