Well as you are talking about an Ops job, you needn't worry about the pilot-hiring side of things (which is what some of the above is about).
On the employment front, they are more likely to be concerned with your skills and abilities than the residency side of things. Some NZ aviation entities actively recruit overseas because the recognise the valuable experience that often comes from with the applicant (the CAA for example). Their website has info on living and working in NZ, all ready for expat applicants.
Nice country here, not as crowded as Dorset is!