I've lived with a kitty-cat in Darwin, so I imagine the sort of diseases etc are fairly similar, given the similarities in climate etc.

Provided you are able to keep up the vacc schedule, the other main things you will need to manage is fleas (using a spot-on treatment on the back of their neck) and a worming schedule - which involves popping a pill down their throat once a month. The worming is really important because there are intestinal parasites in the small creatures (like lizards etc) that they eat. But I imagine the risk from a vaccinated, treated cat is much less than from having rodents running all over the place. It might be worth ringing a vet somewhere like townsville or darwin, as they will have a better idea of what you would need to do than one in the southern states.