There was ONE Hurricane in Australia. A few more on the other side, Burma, India etc.
There were numerous Spitfires in RAF and RAAF service in and around Australia, and through the Pacific. The Royal Navy Fleet Air Arm operated
Seafires in the latter stages of the Pacific war, and there was a shore base in Australia where they operated them as well.
In addition, the RN FAA operated Avenger, Corsair and Hellcats.
You can get a Spitfire
off a carrier, proven several times in the Med, but getting one back on, without a hook would be problematical.

Even with a hook, the unsuitable Spitfire undercarriage, and various other nasty deck-landing characteristics proved it was hard enough to land a Seafire on deck, as the loss rate due to deck landings at Salerno proved.
AFAIK there was no official use of Seafires or Spitfires by the USN aboard carriers in the Pacific, although there's no reason that a RN Seafire couldn't have landed on a US carrier.
Over to those knowledgeable on the USN.