As far as I’m concerned, Australia has no need to become a Republic. The Queen is a historical figure and her position as Head of State is a ceremonial position and nothing more than that. The Queen doesn’t have any say in the politics of the UK, let alone Australia – she’s an aging tourist attraction.
Don’t fix it if it ain’t broke seems a valid phrase here. No matter what banter goes on between the UK and Australia, they are strong allies and friends. Australia becoming a Republic may cause unncessesary tension between between the UK and Australia.
Australia is a soverign-state which in any realistic terms has complete self-rule and the fate of the nation lies entirely in their own hands. The country has largely a British heritage and Queen as Head of State has valid ceremonial perpose – it’s nothing more than remembrance.
Of course, if a referendum is held and the Australian people choose to become a Republic, that is their choice and no one elses.
The Queen doesn’t get involved with any matters of trade, or politics.