Queen's Birthday was the first Monday in June, so was a fixed day, but not a fixed date. As King Charles was born in November, that may change, or may not, for some places.
26th January (controversial)
ANZAC Day = 25th April — Australia and New Zealand, but incorporating veterans of all nations from many wars.
11th November is a commemoration, but not a holiday / day off. Labour Day is a holiday, but not fixed nationally.
5th November is celebrated (where fireworks are still allowed), but is not a day off type holiday.
You already mention Boxing Day, and the 1st January.
Other Australian fixed holidays are fixed days, but not fixed dates (such as Easter), so harder to pin down.