Rabbits travel most safely by car in a secure, well-ventilated carrier rather than loose in the vehicle. The carrier should be lined with a non-slip surface and familiar bedding, and ideally secured with a seatbelt so it cannot shift during braking or turns.
Rabbits are highly sensitive to heat, and the Rex's dense coat compounds this risk. A vehicle should never be left to warm up in sun, and a rabbit must never be left alone in a parked car, where temperatures can climb to lethal levels within minutes. Aim for a cool, stable cabin temperature.
Because travel is stressful, offer familiar hay and a water source, keep noise and handling to a minimum, and plan quiet stops on longer trips to check on the animal. Many rabbits will not eat during transit, so monitoring appetite afterward is important since prolonged anorexia is a medical emergency in rabbits.