You need to get familiar with the routes towards a visa that lead on from this page.
http://www.immigration.govt.nz/migrant/stream/work/
1. Possibly your partner would have enough points to put in for Residence under the Skilled Migrant Category. If so, if you can prove you have lived together for at least 12 months, she could put you on her application as a secondary applicant, and you would get Residence as well.
2. If one of you could manage to get the offer of a skilled job in NZ, you could apply for a temporary work visa. This would mean you could sponsor the other for a partner-sponsored temporary work visa
http://www.immigration.govt.nz/migra...milystream.htm, which would allow him or her to take any job offered, and would run for the same amount of time.
What subject was your girlfriend's degree in?