No, you would only earn AA EQM/EQD on AA partners, so NZ wouldn't count toward AA. If you had a UA account, you could credit there (I think they're still in *A). That's one thing you need to watch out for when booking partners, is making sure flights on their partners will still count toward AA status.

A friend of mine who is AA EXP flew in CX PE recently and got an op-up from PE to biz for a HKG-JFK leg. She definitely appreciated it ^