Hey Annika!
Why do you think your German degree is not enough. There are several pre-requisites that one should have before applying and having a Physio degree from a 3 year course of study with at least one year post registration working experience is sufficient.
You should go to their website and download their guidance form for the application process for overseas applicants (Here: Applying for Registration | Physiotherapy Board New Zealand). It truly helped me a lot and they answer most of all the questions you have.
Pat.