A month after we bought our 2003, we towed a Ford Contour 1,000 miles from Houston to Knoxville using a tow dolly off the bumper hitch. Other than a tire with a slow leak, our Trac hauled it just fine. Even though I used a ball on the bumper, I would recommend using a regular tow hitch connected to the frame.
The Trans Am is a little heavier, but it shouldn't be a problem. You could disconnect the driveshaft on the Trans Am if you use the tow dolly, but it's not really necessary with a stick shift car. Just remember to put it in neutral! The car trailer has some weight of it's own, but it should be equipped with some kind of braking system, so that could be a help. Tow dollys don't have brakes, but they are a lot lighter. Check out your brakes before you go. Towing a car with a dolly can really increase your stopping distance! Take it slow and easy, especially when accelerating, and it should work fine. Our Trac has over 100k on it, and I wouldn't have a problem towing with it.
WHo are you getting the tow dolly/car trailer from? U-Haul won't rent a trailer if it's to be towed with an Explorer. Some here have gotten away with it, but it could be a problem.