Upvote:1
From Working Holiday Visas (emphasis mine):
You need to have a return ticket, or enough money to pay for one, and be coming mainly to holiday, with work being a secondary intention.
So, from what you described you would not qualify for a NZ working holiday visa.
You would need some kind of work permit, because you certainly can't do that on a tourist visa. It's possible that you could arrange a short term work permit in NZ, but that would probably require them to "hire" you as an employee in NZ.
In my opinion, it's unreasonable for the Australian company to ask somebody on a working holiday visa to leave the country, even for a short work trip.