Sway bar for wolf pup?

You can try towing without them, see what happens. But if you experience unwanted behavior, be prepared to install both. I'd surely try it first without. I loaded my flat utility trailer with more than 3369 pounds and towed it with a Chevy S-10 many, many years ago. Never had a problem. Try it, see what happens. Chances are, you'll be OK.

You will need brakes on the trailer and a brake controller in the truck though. No getting around that. (Indiana requires brakes on any trailer with a combined weight of trailer and cargo over 3000 pounds).