Most trailers for towing animals have proper suspension with shock absorbers. Most TT's dont have shock absorbers so i would think if you were at the front of the trailer riding mostly on the trucks suspension i would think it would not be as bad but anywhere from the wheels back must be like a bouncy castle. Guessing the bigger and heavier trailers would be better. Might be opening the door to a green dog.
If you have a 5er and want to keep them in the bed you can still get a good size dog crate under the overhang. Not sure what the turbulance would be like though. I have had the plastic level squares fly out of there once. Never thought that would happen.
I fold up the seats and put big camo blankets (from Cabellas, they are awsome) over the seat and floor so the dog hair removal process later doesnt take two weeks