Time spent living together can sometimes be added up to prove a relationship. You don't have to have a set home in order to show that you're in a live-in relationship (some people have collected their partnership proof while travelling together), but you have to be able to provide evidence that the two of you are mutually dependent, live together when you can, and keep up the contact when you are unavoidably apart. Whether or not INZ will grant a visa yet depends on things like how good your proof is and how long together it shows. Here are some old threads about partnership which may give you some helpful ideas.
https://www.google.co.uk/?gws_rd=cr&...tnership+proof You will see, it's showing that when you're together, you actually
live together, that matters. Because partnership visas are the ones most often targeted by fraudsters getting NZ citizens and residents to lie to get them visas, INZ don't accept just what people SAY about one another and their relationship - partnership is counted as the one aspect that can be objectively proved.