As an Australian citizen, you're able to land and take up any job you're offered straight away, so this gives you an advantage not shared by all those on here who have to get an appropriate visa if they can. (However, if you had any police record you'd have to declare this and apply to INZ in advance.)
It's not a good idea to arrive immediately before the Christmas/New Year holidays, hoping to pick up long-term and/or qualified work right then. Many businesses in NZ take a complete break over the holiday, and/or have only a skeleton staff, right through till the start of the new school year around the beginning of February, so chances of putting in a job application and meeting the decision-makers are really low at that time. But it depends on the industry - if you're wanting a non-qualified fill-in position, you might get taken on in something connected with leisure or holidays, just for the season.