Late reply, but I think it depends on what the allergy is. If triggered by shavings, for example, you can either not bed the trailer for a short haul or for longer haul or with one that pees, you can use paper shavings or something else to reduce pine dust. If a long haul, does your shipper do layovers and is the pee/ammonia regularly cleaned out? Fans in the trailer?
Overall, I wouldn’t be particularly concerned about hauling unless stress is a major trigger and your horse is particularly stressed by hauling.
