In fact, the continent was still known as New Holland in 1788.
So, Australia did not exist in name even in 1788.

So, yes under the same misguided logic you could choose the date Captain Cooke claimed the eastern seaboard of New Holland on August 22, 1770. There is no difference between January 26th and August 22nd.

http://www.nma.gov.au/online_features/defining_moments/featured/cook_claims_australia

Some Historic Maps of New Holland
http://www.acmssearch.sl.nsw.gov.au/search/itemDetailPaged.cgi?itemID=404927

Nah, shifting it to Dec 31/Jan 1 is a silly idea because it gets in the way of New Years.

April 4, 1817 was the first time the continent was officially referred to as Australia. This is a much better date, even though it will occasionally get in the way of Easter.

New Holland was Australische for the Dutch.

" A Terra Australis "land of the south" appeared on world maps from the 15th century, . This theory of balancing land is on record as early as the 5th century on maps by Macrobius., a fifth-century Roman philosopher.

The Ancient Greeks conceived the idea of a southern landmass to counterbalance the land in the north. Aristotle named this imagined southern land ‘Antarktikos’, but his birthday is unknown and "Aristotle Day" is not easy and may be swearing. Yanks say "Arstralia", the Queen "Horsetrailia".

1625 in "A note of Australia del Espíritu Santo, written by Sir Richard Hakluyt", for an island in Vanuatu,. The Dutch Australische in 1638, to refer to the newly discovered lands to the south.

The name Australia was specifically applied to the continent for the first time in 1793 Zoology and Botany of New Holland,.

31 December is a work day, its not a public holiday.

In terms of the Summer Solstice it is pretty close to Canada's July 1.
It would also provide us with a 4 day weekend in certain years.

Canada needs the sun.
The Australia Day prison didn't get built until construction on Darlinghurst Gaol wall began in 1822.

On 22 August 1770, James Cook claimed the coastline as British territory and first named the land " New Wales", with the birthday of
Edward I being 18 June 1239. He put English boots into Wales in June 1276.

//31 December is a work day, its not a public holiday.//

I know. But since there is already a public holiday on New Years Day, we don't need one on New Years Eve. Two public holidays back-to-back is a waste.

I'm used to the public holiday being where it is, but I've no objection to shifting it - as long as it doesn't get lost or wasted in the process. Shifting it to a rubbish date for reasons of pomp and circumstance and tradition is complete f*&king bollocks. Shifting it to a new date that is practical is fine. 4/4 is good, but there is always the Easter issue. I reckon a date in early September would be the best choice of all.

Now we just have to find some pointless milestone to celebrate in early September and we're set.