2003 B3000(3.0l engine) 4x2(2WD) Supercab with automatic weighs 3,200lbs, with no driver or any other load.
GCWR(gross combined weight rating) for above truck is 7,500lbs
7,500 - 3,200 = 4,300lbs load, including driver, passengers, bed load and trailer(dolly) load
4,300 - 3,400(Audi) = 900lbs for driver, passengers, dolly, and bed load.
Trailer hitch looks to be class II so rated for 3,500lbs, so OK for Audi, but..............
Because it is the same weight as the truck, and as alwaysfloored point out, it will be pushing the back end of the truck around when slowing down, especially if slowing down when going around a corner.
So do all your slowing down on straight a ways NOT corners.
Do not store any thing IN the Audi, it needs to be as light as possible, put any load in the bed, and do not exceed the 900lbs including driver, if you have a passenger that has a drivers license you would be better off having them drive the Audi
Automatic transmissions fail because of heat, you need two transmission coolers, for sure, the one in the radiator is not enough, if you have a factory towing package you may already have this, look under the truck in front of the radiator that is the usual location for factory added trans cooler, it you don't have one get one, or you will burn up the trans pulling that much weight long distance, it will overheat trans fluid.
Another option to save the wear and tear on your truck is to see how much a 1-way ticket is, i.e. airfare, trainfare, ect........, weigh that cost against what dolly will cost you(assume it is a rental), and the extra fuel cost for towing.
Then cost of 1-way ticket and fuel for the Audi.
EDIT:
3,200 + 2,000(u-haul) = 5,200lbs
7,500 - 5,200 = 2,300lbs load
Put heavier stuff IN the truck.
U-haul Trailer will have a tongue brake which is a "react" brake, so same as above, do as much slowing down on strait a ways as posible.
Second Trans cooler is still needed