If I can add:
Some also grows in the Southeast of the mainland.
It's Nothofagus Cuninghamii, the oldest tree in Australia in evolutionary terms. You see pure stands in Tasmania that are eerie to walk through. Those forests go back to Gondwanaland some 40,000 years ago IIRC; when the continents split the Beech also evolved in New Zealand where it is now a distinct species.
Regrettably the Tasmanian Beech is also being cut for woodchipping. At the current rate of exploitation there'll be little left for turners and furniture makers in a matter of years.