FWIW, I used to haul a drag car and trailer around using C-bodies and had pretty good luck. Probably around 5500 lbs loaded.
Trans cooler is a good idea and if your trailer has electric brakes, look at some of the newer brake controls. The amount of adjustability, control, ease of installation etc. is tons better than the ones I struggled with in the 70's.
One thing that does need to be looked at is the rear frame rails. You don't want to bolt up a hitch to a rusty frame rail.
Speaking of hitches, I'll agree that a Class III receiver type hitch will be best and will have the most versatility, even if you don't plan on hauling the weight they are rated for.
Trans cooler is a good idea and if your trailer has electric brakes, look at some of the newer brake controls. The amount of adjustability, control, ease of installation etc. is tons better than the ones I struggled with in the 70's.
One thing that does need to be looked at is the rear frame rails. You don't want to bolt up a hitch to a rusty frame rail.
Speaking of hitches, I'll agree that a Class III receiver type hitch will be best and will have the most versatility, even if you don't plan on hauling the weight they are rated for.