An Australian republic would remain a parliamentary democracy just like we currently have. But instead of having a Governor General representing Australia’s head of state - The Queen of England - we'd have someone representing the Australian people. The PM would still be in charge, but we'd have a head of state representing Australia and carrying out constitutional duties.
The Australian Republic Movement is campaigning for an independent constitution, with an Australian citizen as head of state with similar powers to the current Governor General. At the moment we are focused on the question, ‘Should Australia have an Australian head of state?'. Once we've built consensus on this, the public will have a say on how an Australian head of state is chosen.