Yes, all Airpasses are issued in 'Q' class. Thats one of our less discounted fare classes in general so I'd be surprised if you didn't earn miles on it.

Wellington's a lovely place, I'd certainly recommend a visit - you could check out Te Papa (the Museum of NZ, which is somewhat different from traditional museums - think coin operated historical rides, etc) and take a ride on the historic Cable Car, which has been operating since 1902 and takes you up a hill that has a great view of Wellington. It's also one of our more 'interesting' airports to land at - water at one side, high tension power cables at the other, and a black star rating by the ALPA

Sorry, I completely forgot to point out, as the earlier poster said, that you MUST purchase this ticket outside NZ - have your international ticket number ready. Had a situation the other day where someone called from the gate at SYD, just about to board the plane, and we had to contact Sydney to ticket it before he boarded! Talk about stress

One place noone's mentioned so far is the Bay of Islands - one of my favourite places in the world. You can fly directly there from AKL (the airport is Kerikeri {KKE} and the flight is operated by a Bandeirante - which is always fun). It's full of stunning scenery and history (it was the scene of NZ's first capital back in the whaling days (Russell, then known as Kororareka). You could even continue right up to the top of New Zealand - Cape Reinga. The Maori people believe this is where the spirits depart for their mystical homeland, Hawaiiki, and you can see the Pacific and Tasman seas meet.
http://www.fullers-bay-of-islands.co.nz/ is a good site to get an idea of what I'm talking about! I'd highly recommend the 'R. Tucket Thompson' or 'Cream Trip' cruises.