The only overseas, non Australian territory allowed to use it!
Not so!
The Kiribati Republic also uses the Australian Dollar as their official currency.
Tuvalu also uses the Aussie Dollar banknotes whilst having their own coins as part of the Tuvaluan Dollar. Both Tuvaluan coins and Aussie coins are in circulation together.
Kiribati and Tuvalu were once part of the Gilbert and Ellice Islands.