@eatham @unionagainstdhmo Perhaps the date of proclamation could work as a national holiday?
"The Proclamation Declaring the Establishment of the Commonwealth was a royal proclamation made by Queen Victoria on 17 September 1900 federating the six separate British colonies of New South Wales, Queensland, South Australia, Tasmania, Victoria and Western Australia under the name of the Commonwealth of Australia."
Another option would be 3 March, when the Australia Act passed, which effectively ended British rule over Australia:
"The Australia Act ended all power of the UK Parliament to legislate with effect in Australia – that is, "as part of the law of" the Commonwealth, a state or a territory (s 1). Conversely, no future law of a state would be void for inconsistency with (being "repugnant to") any UK law applying with "paramount force" in Australia; a state (like the Commonwealth) would have power to repeal or amend such an existing UK law so far as it applied to the state (s 3). State laws would no longer be subject to disallowance and reservation by the monarch (s 8) – a power that, anomalously, remains for Commonwealth legislation (Constitution ss 59 and 60).[n 6]
...
"The Acts came into effect simultaneously, on 3 March 1986."