In an emergency, how much runway does an A320 need to stop safely?
Airbus's charts for the A320 suggest that it requires approximately 4,500ft for a sea-level landing at typical landing weight. I've extracted this from this Airbus document (the A320 landing chart is on page 49), which is admittedly more of a promotional brochure than an operating manual.

Wellington's runway is 5,955 ft between thresholds, and 6,827ft overall, so there is some room for error. However, depending on the nature of the 'flat-out emergency' a pilot may approach faster implying a longer landing roll, or choose a firm landing and significant abuse of the brakes to shorten it.

Christchurch and Auckland airports both offer much longer runways at 10,787ft and 11,925ft respectively, so I'd speculate that a pilot faced with a known problem with brakes or thrust reversers might elect to divert there if range permitted.