I just did mine by post. I can't remember how long it took exactly, but it was a matter of days (maybe a week and a bit) rather than months. Obviously the NZ embassy have seen all this many times before due to the number of cadets CTC send out, so if you follow to the letter all the instructions CTC have given you, you won't go far wrong. If you're going down there in person, I would suggest ringing them beforehand. PM me if you need any more help.