Throughout the ship, casual resort wear, sundresses, shorts, polos, or button-downs are appropriate, paired with sandals, low heels, and loafers. Good walking shoes are important if you want to take advantage of the wonderful hiking in both countries. Pack sunblock and a sun hat as the sun is strong here.
In Australia, the north is humid and tropical, and the south is more temperate, generally speaking.
Generally speaking, New Zealand is cooler than Australia.
Australia and New Zealand cover a vast area, so pack according to the climate zones you are visiting.