Yes, you'll have to do paper forms. Here
https://www.google.co.uk/#q=site:enz...tnership+proof are old threads that will give you ideas for different kinds of evidence you can submit. The easier you can make it for the CO, by providing lots of evidence all laid out and plain to understand, the more quickly they can deal with it. Keep collecting partnership evidence, because INZ will ask for more just before issuing the visa, to cover the time while it's been being processed (guarding against giving a visa to anyone whose relationship has broken down in the meantime). Then keep all that evidence, and collect more routinely, because you will need 12 months'-worth to put in for her Residence.
The INZ London branch say
http://www.immigration.govt.nz/branc...ocessingtimes/ it can be done in one to three months - partnership visas are given priority. NZ like to have their kiwis come home.