From what I can see on the official NZ Department of Immigration website you partner's visa will be granted for the duration of your course, provided you can produce all the documents to support the visa application. If your course is three years long and you have a student visa for that period of time, hers should be granted for the same period of time.
I am afraid I can't find any concrete information regarding what would happen if you guys were to have a child over in New Zealand. You should maybe contact an immigration specialist to check this out.
For more info read the Visas for New Zealand page.