The governor-general is going, come on the republic
The Sydney Morning Herald has a graphic of selected heads of states, how they're appointed and what they do. Now, I know it's a bit radical for the twenty-first century but I think the people should elect the head of state. The model where the governor-general is elected by an electorate of one is broken, let's fix it.

Before finally deciding this is what I believe I did extensive googling to try and track down how often the elected non-executive president overthrows the prime minister in Iceland and Ireland but damned if the evil swine haven't managed to keep all record of the constant streams of presidential coup and counter-coup in Iceland and Ireland off the Internet.