Does JQ offer the piece system for baggage from North America? Otherwise the bigger problem is the weight allowance and the few hundred dollars of overweight fees you are likely to face.
I have never transferred at AKL but I doubt that JQ will have a baggage recheck at international; you'll have to carry the bags over to the domestic terminal (which isn't far) and go through the JQ check-in process as if you were originating in AKL. Ironic isn't it that interlining with NZ would be easier than with JQ? Got to love the convoluted business model that QF management has come up with -- all to skirt the rules and regulations, and nothing to do with improving the customer service. So much cleverness being completely wasted.