The Defaced Blue Ensign
(official title of the Australian flag)

Australia's 'flag' was selected from 32,000 designs submitted in response to a magazine competition. The first Prime Minister, Edmund Barton, announced the winning design in Melbourne on 3 September 1901. 

King Edward VII formally notified the Australian Government of the approval for using this ensign as our first Federal flag and this was finally Gazetted on 20 February 1903. The flag underwent several modifications over the next decade.

However it still was a British Admiralty flag, and legally to be used only at sea and subject to conditions specified by the British Admiralty until 1954 when Australia's parliment enacted the Flag Act of 1953.

During this intervening period (1901-1954) Australian Servicemen fought under the British Flag - or the Civil (red) ensign. 

(the civil or defaced red ensign)

Advertisements for recruits during both world wars depicted only
the Red Ensign or the British flag.

The Australian flag flown during the opening ceremony of Australia's First Federal Parliment house in 1927 was the Red Ensign.

Until 1967 the Australian Navy still flew under the British Naval Ensign.

The RAAF used the ensign of the Royal Air Force of Britain until 1949, 
whereupon the Southern Cross and Commonwealth star were added to the ensign and the British roundel was moved. 
The Air Force Ensign with its British roundel, however, was not altered until 1982 when the central red circle of the British roundel was substituted with a leaping red kangaroo to create a new Australian roundel. 

The Union Jack on Australia's ensigns occupies the 'Honour Point', which is occupied by the national flag of the 'sovereign owner' of the territory or province over which the flag is flown.

While I am a monarchist, and believe the model for a Republic defeated at the referendum was unsuitable for Australia, I firmly belive we need our own flag.
As for a republic, only if we, the people, actually decide the President.
 

Australia II's Battle flag