When you board the plane try to sleep as the destination time zone. In your flight plan, try to catch some hours of sleep. You will wake up fresher and really to go when you touch down. Although easier to say than done since economy seats are notorious uncomfortable for long haul flights.

I have been flying to US frequently from Singapore to US and the trick of sleeping and waking at the destination time zone while flying has worked for me. I do not need to adjust for so many days when I arrive.

Other tips:

Do not drink alcohol and caffeine drinks too much while flying, they will dehydrate you making you feel terrible. Drink plenty of fresh water instead. Also try to stay away from gassy drinks like coke, they will cause your stomach to bloat in the pressurized cabin although eating too much has the same bad effect too.

Walk around to improve blood circulation.

Do stretching exercise when you can to relieve sore body parts from seating too long.

And stay cheerful since you are arriving in NZ, Yippppeee!! Oh yeah, enjoy the summer and the sunshine while there can also great relieve jet lag!

Pulsarblu