Tow question

I'm no expert, but my opinion for what it's worth... The engine/trans should do the job but will be sluggish in the hills. Get yourself a trailer brake controller and weight distribution hitch to help with rear end squat. As others have said, the suspension might be the weakest link here. If you don't already have the ride leveling system, you could probably get helper springs or airbags for the rear coils to help with squat or bottoming out. They don't increase your payload, but will help you get more out of the rig you have safely. All that said, your truck is 8 years old and will probably not perform to factory-fresh specs, but it should be sufficient to do the job while you shop for the next towing rig.
Enjoy the towing/camping and welcome to the forum!