Don't forget that Australia had a "mean and tricky" monarchist for a PM at the time and made sure that the model that got put to a vote would be too controversial to pass.
There are two types of models that could pass a referendum:
- The McGarvie model - one in which the Queen is replaced by a constitutional council and the GG is called the "President" but nothing else is changed.
- One in which the President is elected by the voters and has some powers which he could legitimately exercise autonomously.
I personally would like to see the PM abolished and the President head the executive like is done in the US but politicians are averse to reforming a system that hands them power.