The cat will not be allowed ashore in any of Oceania. When you arrive in New Zealand or Australia you will be required to keep the cat on board at all times and you will be visited by (?) Animal Control weekly, and you will have to pay for their visit - at a quite pricey hike. Additionally, in Autralia, you will not be allowed to tie up in a marina due to the risk that the cat will escape and get on shore.
Here's a quote regarding some of Australia's rules as reported on The Cruising Wiki
: "Yachts with animals on board may only anchor, and the animal must be kept on board and confined (in a cage or below decks) at all times. Quarantine must be notified of any intention to change mooring at least 48 hours prior to moving, as well as the proposed itinerary in Australian waters. Permission to go to a dock to take fuel or water must be obtained in advance. While at the dock, the animal must be locked below. Permission must also be obtained before sailing to another area. The boat must be locked up whenever the crew is away. If embarking animals in Australia, they must have a health certificate issued by a veterinarian."
New Zealand is even stricter.