The Sunlite 16 BH is intended for drivers who don't want to buy a new tow vehicle. I've seen many videos from PRO reviewers who proclaim the virtue of it being safely towable with Jeeps, Subarus, SUVs, even minivans!. Tongue weight 210, unloaded weight 2600. His Ranger can handle 5,000 so this camper is MARKETED for him. Te 16 BH has trailer brakes and anti sway and if he proceeds slowly while learning, things should be fine.So under #4000 that's 80% you didn't tell about the engine. Yes it will do the job. The truck stops the truck,and a little more,the trailer has brakes!!! Believe it or not.
I can spend your money, but I won't!!! When you come back with the statement you just bought a one ton dually, you will get the approval to tow that much trailer, from this group.
No matter what your told, your learning curve for a first time trailer driver,you will find issues. That said, you are within design limits for your truck.