Upgrading of status occurs each Sunday, so depends when you crossed the line and that happened, last Sunday or this Sunday.

I am awaiting a similar new kit, so will post when it arrives as last Sunday was when my account was "scanned". As I live a few miles from the processing centre, you can then add two weeks for passage through the postal system to New Zealand. I actually expect it would not take a full month, and you should have your card/package by sometime in May. If not, as others suggest, print off your account page before you leave, and that should get you into the lounges you need.