I wanna see a pic!As others have said a car cover on an open trailer is a no-no... however...
You can wrap the entire car with or without the car cover with stretch wrap and packing tape.
Pratt Retail Specialties 12.2 Micron 17.5 in. x 1500 ft. High Performance Cast Clear Stretch Wrap-APPH1880SX at The Home Depot
I've towed cars for hundreds of miles with the car cocooned in stretch wrap and simply cut it off upon arrival and you have a clean car!
Hint: be sure to wrap under the car as well as over and around.