The only reason Australia & NZ are not republics is no national government of either country has given the citizenry a chance to vote on a real Republic model. Both sides like the ability to appoint or reappoint the leader mid term from the party room. The citizens won't vote yes to a replication of this process minus Crown ascent as much of the point of becoming a republic would be in being able to directly elect the leadership. John Howard tried to sell a party room based Republic system by referendum in Australia in the late 90's. It failed, as most pundits will say it was intended to.
In reality we are more beholden to the USA for defence reasons than any nominal ties to the UK would have it. Meanwhile we are getting better at relating to our near neighbours. Time will tell, but I think Oz & NZ are both pretty hard to beat when it comes to selecting a spot to ride out bottle necking.