I had a similar experience to plunet and didn't queue for egates or the bio-security check. The 4am arrival worked well for me, as it meant plenty of time to get to the domestic terminal and connect onto the first wave of morning flights, starting at 6am, which I'd booked as a separate ticket.
I'd easily have made a 6am flight, but would always book the Air NZ "Flexitime" fare so you're covered in-case of delays / queues.