Their are reciprocal agreements between Australia and New Zealand for their citizens in repsect to living and working in each others country.
For you Bill, it would be best to contact the Australian Department of Immigration & Citizenship (
http://www.immi.gov.au ) and/or the New Zealand Immigration Service (
http://www.immigration.govt.nz ). It isn't always necessary to get married, other options available include as a De Facto Partner or in your own right (especially if you have a trade or qualifications that are in short supply in Australia or New Zealand).