If it's a typical stick built box trailer and empty/dry, it will probably have a GVWR of around 5,000 to 6,500 lbs. and put less than 1000 lbs. of weight on your tow ball. No problem. If the trailer is full of fluids, drain the tanks. If it is loaded with all your friend's personal belongings then all bets are off.
For one trip you should be fine. I towed 50 or 100 conventional travel trailers, most of them much longer and much heavier than the one you're going to tow, without a WD hitch when I was transporting. I used a solid steel draw bar and very heavy duty 2 5/16" gooseneck ball on the drawbar on my dually and never had any use for a WD hitch or sway control. If I owned the trailer and pulled it routinely I would use a Reese Dual Cam WD Hitch with built-in sway control devices.
With your Ram 2500 you won't have as much weight carrying capacity or as much sway resistance as a dually offers but you should be fine for one trip. Sway control can become a serious problem when towing in spring winds so have all eight tires properly inflated and be prepared for the effect of strong quartering winds. If the winds get strong slow down, or park it, change routes, or wait until the wind subsides.
There is no DOT requirement to use a WD hitch or sway control unless the tongue weight exceeds the carry capacity of the hitch receiver or the rear tire weight carrying capacity of the tow vehicle.