Huh? Australia has a PM now and it would still have one. The President would be of the mainly ceremonial and titular variety. Like in Ireland and Germany. You do understand that don't you? There are at least two kinds of presidency: the American/French kind and the Irish/German (and Italian) kind. They are radically different from each other. Right now, effectively, Oz has a president (second type) called Elizabeth and its next one has been chosen for it by inheritance. Barring accidents, so have the two after that.
It will make very little practical difference if you replace the Saxe-Coburg-Gothas with Richie Benaud or Germaine Greer except symbolically. If you want to argue that symbols don't matter please explain why there seem to be so many.
Unfortunately the Republican movement has not decided on which model to adopt. The first type might be more popular with the people who may think that a directly elected president would be a good idea, except that may require a fundamental redesign of the separation of powers which is another hurdle as it would require a change to the Constitution. The second type would theoretically be better except that an election system similar to the German/Irish/Italian kind was voted down in the 1999 referendum.
For Australia, the monarchy symbolises an imperial, subservient colonial past, patronage, privilege, deference, hierarchy. An elected Pres. would symbolise modernity, democracy, equality, independence and mature nationhood.
Does this mean the form of government a former colonial power has all these negatives attached to it? Are all monarchies of former colonies examples of this? And does this depend on the form of government in the ruling power when a colony gained independence?
How does a republic represent "mature nationhood"? Is India a more mature nation then the UK? Is Suriname a more mature nation compared to the Netherlands? Is South Korea a more mature nation then Japan?
Why not change your flag to an ocker downing a glass of Fosters?
Because that would be a stupid flag.
Also, tie me kangaroo down sport as your national anthem.
Why would we want to change our national anthem? We just wouldn't have a royal anthem any more.