From the National Australia Day website; Australia Day is for all Australians, no matter where our personal stories began.
Australia became an independent nation on 1 January 1901 when the British Parliament passed legislation allowing the six Australian colonies to govern in their own right as part of the Commonwealth of Australia. The Commonwealth of Australia was established as a constitutional monarchy.
Before 1901, Australia was not a nation. At that time, the continent consisted of six British colonies which were partly self-governing, but subject to the law-making power of the British Parliament. It was a collection of six British colonies which were partly self-governing, but under the law-making power of the British Parliament.
So with the birth of a nation occurring on 1 January 1901, the most relevant Australia Day, in my view, would be January 1 to celebrate the birth of our nation.