On 28 August 1996, The Governor-General of the Commonwealth of Australia, Sir William Deane, acting on the advice of the Federal Executive Council, declared that 3 September in each year would be observed as "Australian National Flag Day" throughout Australia and in the external Territories of Australia.
While Australian National Flag Day isn't a public holiday, it is a day to commemorate the day in 1901 when Australia's National Flag was first flown.
Go to the website for more information.