As no one else has answered yet thought I would attempt. I don't think you can convert your PPL as it is not a Professional Qualification under the Trans Tasman thingy like you can with a CPL however I'm sure you can just get your NZ PPL Validated through a flying school for a period of time, probably involves a quick check flight and a short quiz. I will probably be corrected by someone better in the know but that's how I think it works with a PPL.
Have fun