"As far as I know, there are no current restrictions for the A320 to operate in to or out of Wellington."
Not for the Air NZ ones there aren't.....now. Air NZ use a computerised Take Off Data Calculator system that ACARS' the TOD to the aircraft (or Flight Planning room) Without this system (which I believe Jetstar don't have), using the tabulated figures from the individual runway take off charts, there were payload restrictions on RWY34. Admittedly these were for trans-Tasman flights. I don't think there would be any problems with domestic fuel loads.
This system made a huge difference to the amount of thrust reduction available on take-offs on all runways (with associated fuel and maintainance cost savings) and meant basically unrestricted loads out of PMR, DUD (03) as well as WLG (34).