There have been people granted a visa on the basis of around two months' GOOD and PLENTIFUL evidence. See old threads
https://www.google.co.uk/#q=site:enz...tnership+proof for ideas, and taking the collecting of this VERY seriously. Several pieces of evidence of different kinds, showing you are both living there together and going about together as a couple, for every passing WEEK. Remember you will need to keep on collecting after the application has gone in - INZ will want proof you are still together while the processing is going on, and afterwards, for residence (which needs 12 months' proof, this first part counting in as well, so keep photocopies of everything, and detailed records).
Notice, you can't be certain your application will be processed in only a month, and/but as long as you put in your application while you are still covered by your existing visa, you will be granted an Interim visa if INZ haven't finished processing before your expiry date, to keep you legally living in NZ meantime, but it won't give you the same rights as your present visa. See here.
https://www.immigration.govt.nz/new-...isa-conditions