There are no restrictions associated with traveling with a kayak trailer. Since you will most likely fly with kayak only and drive long-distance with a kayak trailer attached to the car, traveling is not off the radar for paddling enthusiasts.
Before embarking on a faraway trip, however, you need to make sure your kayak trailer’s weight stays in the safe towable limit, and your watercraft is properly secured. In case you are planning on flying, check with your airline’s guidelines before arriving at the airport in order to avoid any unpleasant ‘surprises’.