USA, I believe the civil war was over their wish to have self rule and kick the British out! Australia already has this, it was done much later and more peacefully because the British knew they could not stop it and faced another USA style war if they tried but much further away and harder to support.
"The British"? Sounds like a modern mainstream perspective that makes them sound like foreigners, when they were not. In the 21st century we are accustomed to having distinct national identities (despite the persistent close ties, common history, language, culture and other massive similarities), but it wasn't always so. They may have been referred to as "The British" in non Anglo-Saxon territories like India and elsewhere, but the Anglo-Saxon colonists were British and mostly considered themselves as such, including in North America, and probably moreso in Australia and New Zealand. The American war of independence was a form of English civil war, not a case of all or even a majority of colonists versus "the British" as an evil, tyrannical foreign power. When British soldiers marched on North American soil they were usually referred to as "the regulars" or "redcoats", not "the British", because they were all British.
On the subject of self rule, to say that the British "knew they could not stop it" is probably not an accurate reflection of the time. Despite a republican movement of sorts that dates back many years, in the late 19th/early 20th century Britain was not seen as a foreign power that had to be escaped, except by a few crackpots on the fringes; the colonies had already had extensive autonomy for decades. If there was less than 50% active support for American independence in the 1770s, how many "Australians" do you think would have been willing to fight for a republic in 1900? Until 1949, "Australians" were British subjects only, not Australian citizens, i.e. they were British; many were born in the UK or only first or second generation colonials. Just when did Australia become independent, anyway? The Commonwealth of Australia was created as a British colony by an act of British parliament. It's a popular myth that Australia became an independent sovereign nation in 1901, but it was a largely self governing colony and a major part of the empire. Later, the links were mostly broken by the UK itself, such as when it joined the European Economic Community in 1973 and earlier passed legislation elevating the status of dominion governments without reason to believe it was necessary to avoid revolutionary wars.
So what happened to the ........ United States shortly after they became a republic?Overall taxation roughly tripled as it became "self evident" that running and defending a country was not so cheap after all (but at least the [wealthy / land owning male] citizens now had representation...

The Commonwealth government in Australia also had weak beginnings but became more powerful relative to the States with interpretation, reinterpretation and arguably misinterpretation of the constitution, coupled with (at State and Cth level) the proliferation and complexification of law and the growth of government bureaucracies to help keep individual freedom in check. Mission creep at its finest.
It doesn't do to say any of the above in certain circles, of course. Can't let freethinking get in the way of official creation myths.
Australia may become a republic one day, but the question is more commonly a political decoy, intended to cause an uproar big enough to hide whatever other embarrassing problem the asker of the question is responsible for.Agreed.
My view on the republic is that while it might sound good, even to me, it's essentially a waste of time at the moment because short of a revolution we will not be given a model that really benefits ordinary citizens. It won't really be more democratic. It won't really be more fair. Due to global economic and political ties, it won't even be more independent. It will, however, be expensive. The stirring of nationalistic sentiment and emotional arguments conceal the underwhelming reality of the Australian republic. My support for a republic is on theoretical, idealistic grounds, but my opposition is on practical grounds - grounds of real power that trump republican symbolism. It is not a question of the ability of an Australian to be head of state - that question only seems to rear its head in fallacious republican arguments.
As for the GG's comments, I accept that she is entitled to her opinion as a citizen. However, I don't think it is appropriate for such a view to be expressed in an official capacity as GG. Judging by comments online, Bryce has upset quite a few people.