Do New Zealand white rabbits carry the dwarf gene?

New Zealands don't carry a dwarf gene. Dwarf breeds are under 4 lbs. and include Netherland dwarfs, Holland lops, Jersey woolies, lionheads, etc. New Zealands are a meat rabbit that get to be 9-12 lbs. so there's no dwarf gene there. Runts can be surprisingly strong and get right in there and compete for nursing. You can try allowing the runt to nurse by itself before the rest of the litter, to help it out. But be aware that there's a chance it won't survive no matter what you do. Rabbits have mulitple litters of many babies because not all of the babies are destined to survive.