Well to do that we would need to hold a referendum, and passing something by referendum is hard. It is where policy goes to die. Basically we have this rule where to pass it needs a double majority, that is the majority of voters over all, as well as the majority in the majority of states.
There was actually that very referendum in 1999, where as I recall we got a 45% yes vote over all, but I don't remember how the states turned out. It is interesting to note that the proposed new political system was described as a 'minimalist' republic, and many republicans encouraged people to vote 'no' for the sake of getting a better deal later on, so with public attitude generally moving away from royal ties over time and the chance for a more solid system you never know what turn out will vote for it.
Point is it isn't a hot topic right now, people are a little distracted with boats and the cognitive dissidence of being told the economy is crap despite everything pointing otherwise. Still, you never know when it will show up again. Greens are strongly pro-republic and they are looking at picking up another four senators for a total of ten. Might become a wedge issue next election, who knows.
I will say that the fight in Scotland has sparked a little talk over here. Escaping the royal talons might inspire some more confidence for us to do the same, at the same time if we do go republic any time soon I hope it can bring some more hope for you guys.