Australia is around the same age as America but we called upon an older, tested system on which to base our laws. ...
Yeah, mostly no.
* While the Dutch, Spanish, and English explored parts of coastal Australia in the 1600 and 1700s, the first permanent settlement, plus or minus shipwreck survivors and some marooned mutineers was a penal colony in New South Wales. This was in 1783, when Britain could no longer transport criminals to what had become the United States.
* For over a century Australia was geographically semi-separated colonies mostly dotted along the coast. The colonies were separated by geography but connected by ships.
* The process of Australia becoming a sovereign dominion started in 1901 and culminated in 1907. The UK had learned its lesson in the 1770s and 1810s, and as with Canada, this process was done peacefully. There are quite a few years between 1776 and 1901 (or between 1783 and 1907).
* In the reality of which the poisonous
canetoad seems unaware - or about which (s)he is lying in the hope US DU-folk are unaware - US laws are based on English Common Law, the precedents of several centuries of English court decisions. As for the US Constitution and Bill of Rights, Brits could complain the much is plagiarized or derivative from the Magna Carta, Petition of Right, and Declaration of Right//Bill of Rights.
* Ironically, a war was fought in England between the Petition of Right and the Declaration of Right due to James I tyrannous rule. James lost his head, and ultimately the Stuarts lost the throne. It's funny how English kings' tyrannous rule led to wars and loss of power.