Mind you, 30 January would also do:
On that day in 1813, the word "Australia" appeared in print for the first time. This pre-dated that Flinders use, the one that second-rate politicians cite, later that year.
Here is the passage, in a rather dreadful piece of "poetry": note the fourth line.
FROM Albion's blest Isle have we cross'd the wide Main,
And brav'd all the Dangers, of Neptune's Domain—
The Hurricane's Whirlwind, the Tempest's loud Roar,
An Asylum to find on Australia's rude Shore
For the Genius of Britain sent forth a Decree,
That her Sons should be exil'd—once more to be free!