The states of Australia do a lot of things differently.
Western Australia goes to Daylight Savings at a different time to everyone else, Queensland have Labour Day on the 4th of May, we all have different public holidays for our big horse races (WTF?). etc etc
It's called Commonwealth Day in New Zealand because Labour Day over there is actually at the end of October. Can't explain the Tasmanian one, but they're all freaks with two heads so who cares
BTW Australian Labour Day was actually yesterday