No, you are not required to carry insurance coverage on your travel trailer. A travel trailer is not the same as an RV so it does not fall under the same insurance needs. When towing your travel trailer the liability extends from the towing vehicles auto policy. However, once the vehicle is parked you will not receive the coverage extending from the automobile. This is why we always recommend carrying a separate liability insurance policy for your travel trailer.
Your travel trailer is considered road legal so long as it is being towed by an insured and registered vehicle. You can also carry a specialty travel trailer insurance policy to ensure you will receive coverage on the trailer no matter what it is being used for.
For an RV or motor home you are required to carry an auto liability policy because the vehicle is able to be operated independently. You may also need to add a property insurance policy if you live out of your RV or motor home.