If you have the 5.3 V8, it should do the job. I'm sure you know that TT will put you right at truck's towing limit. You will likely add more than 500 lbs to trailer wt. You will need to have some water on board while traveling, I am thinking you'll add 1,000 lbs minimum to trailer for that length of trip.
Everyone has a different comfort zone, when it comes to towing. That camper appears to be a bunk house, and you don't say how many passengers will be going on the trip. Everyone/everything in the truck counts against the truck's GCVWR.
Anyway, when towing right to the vehicles limit, some will say it was a nightmare towing experience, and the next person say the tow went really well.
Jerry
