urgh, side trip? NRT-AKL? I hope you do know you're talking about a 10 hour 5,500 mile flight (and of course even more if you're flying CX or QF and take a transit). And it's high season down there. Expect to pay USD1700-3000 for an Air NZ discount ECONOMY ticket between Christmas and the first week in new years.

I suggest you contact your local BA office for a RTW fare. Wild guess, but a 4 cont OWE or Global Explorer in C might be around USD4-5K. You should also try calling SQ, SR and other airlines and find out if they offer RTWs.