Reading the Australian Constitution is little help at all. If you took out direct reference to the name of our nation, you’d think it was describing some other nation altogether.
In practice, the Australian people elect the parliament; the members of the parliament elect the executive, including the Prime Minister.
Due to the fact that politicians organise themselves into parties and nominate leaders of those parties prior to elections the illusion is created that we are voting for a Prime Minister, when we are actually voting for a member of Parliament who has indicated who they support as Prime Minister, the leader of their parliamentary party.
This cements the sovereignty of the Australian Parliament as the government of Australia. The Prime Minister and their Ministers are answerable and accountable to the Parliament. The Parliament can change them as it wills.
The members of Parliament will choose a Prime Minister who they believe can best serve the nation, and also best ensure their own re-election.
Where it all gets a bit grey is where outside influences come to bear on members of parliament to make any changes.
If the public don’t like their choice of leader, the public can change their parliamentary representative.
I never thought I’d want Australia to be a Republic. I feel ripped of TWICE this year in elections!