Yes, even on Convict Day - January 26th.

No if they had 7 or 14 year sentences begun in 1787 or so then convict's day was around 1795 or 1802.

Apart from political considerations and sensitivities, the early part of the year has too many holidays. The later part of the year has few holidays.

It would be infinitely more sensible to move the date to the later part of the year and just make it a general holiday for all Australians to celebrate being a nation, without all the imperial and genocide baggage attached to 26 January.

So, you would opt for the 17th of September then - I would be happy with that. But, would the weather be too cold? Not sure.

DECLARATION OF THE COMMONWEALTH
Queen Victoria, Proclamation, 17 September 1900.

We do hereby declare that on and after the first Day of January one thousand nine hundred and one, the people of New South Wales, Victoria, South Australia, Queensland, Tasmania and Western Australia shall be united in a Federal Commonwealth under the name of the Commonwealth of Australia.
http://exhibitions.senate.gov.au/pogg/origins/declaration.htm

The one thing certain about the date is, that like the anchor thrown overboard from HMS Sirius in Sydney Cove on that morning, truth likewise resides on the bottom of Sydney Harbour and has remained there ever since.

Anyone thinking that we became an independent nation when Federation visited us in 1901 is also sadly deluded. We are nothing more than a British Colony and will stay so until someone has the testicular fortitude and heart to cut the apron strings to HM QEII, her heirs and successors.

//We are nothing more than a British Colony and will stay so until someone has the testicular fortitude and heart to cut the apron strings to HM QEII, her heirs and successors.//

They already have. They did it in 1986, with the Australia Act. You should look it up.