I would occasionally to a motorcycle and other race track equipment on a harbor freight trailer when I didn't want to use my big trailer. Probably similar in weight to you. I was usually the only occupant in the vehicle. Mine was a 6MT but I would have no qualms at all about using a DSG. You can barely tell you have anything back there.
I would think more about total weight than the weight of the trailer. If you have 1500lbs on a trailer, four adults, a full trunk, etc, that may be a different story.