An Australian 'Republic', as opposed to the USA 'Democracy'
is entirely different to 'Northern Hemisphere' Republics.
Remember that most crucial point.
In the southern hemisphere - Politics is 'people' based. Not 'individual'.
In other words: Politically, in the North - the 'Power' goes to the Leader (Individual). USA - the Political People are sacrificed for the good of the Leader (President) ...and the Artistic 'leader' is sacrificed for the good of the Artistic 'people' (Hippies, whoever).
In the south - the Political Leader is 'sacrificed' for the good of the Political People. Here in Australia, the positions of PM (who serves the USA) and the G-G (who serves the UK) will be the 'sacrifice' (on the Southern Cross<crucifix>) for the Common 'wealth' of the Common 'people'.
The Art industry here would be reverse and the 'power' will go to the Artistic 'leader', at the expense of the 'people'.
It's the same scenario as in Religions. Like what makes the Catholics different to the Protestants and the Orthodox different to the Pagans.
So with Australia as a Republic (a Southern Hemisphere one).
A 'Chairman' would 'Head' the Republic (Asimov worked this all out in his Foundation series) - but he would be the weakest link, for he/she would be representing on behalf of the rest of the World, or the International arena.
It will be the Political 'Parties' that hold the true Power. A Political 'collective' of Power on behalf of Australia 'directly'.
Remember when all the States were one Party and the Federal level was the other Party?
Occassionally the States band together and would 'jilt' the Federal level on behalf of Australia as a priority - not the International community.
So by becoming a Republic - Australia is 'jilting' the International dominance over this country and switching the priority to 'domestic' wellbeing.
In doing this, a lot of International Nations won't like being 'rejected' (Like China, who has the PM making sure that it's products have priority over Australian ...and you've all seen that happen).
It might even result in 'violence'.
So you can continue to be a 'Convict' for the World.
They will feed you, give you a home, etc ...as long as you do 'their' work for them.
Or you can stand up for yourself when the time comes.
Remember Conan the Barbarian. When he was 'released'.
Everything soon changed when the Wolves started coming for him.