A 30 foot TT might weigh something just over 6000 pounds to in excess of 12,000 pounds. What pickup is going to depend on your choice of trailer.
Engines are not really the issue. Pickups rated for 1200 pounds load and 5000 towing might share engines with pickups carrying and towing twice as much; by the time it gets up to three-four times that, the engines are usually unique to the heavier trucks.
The big factor in what you can tow is not power, it is what thre frame, springs, axles, wheels and tires can carry, and what loads the steering gear can handle. The weight of a trailer on your bumper is a heavy load for a light truck, particularly getting up to 30 feet.
My own choice, for a trailer up to about 6000 pounds, is a 1-ton single rear wheel truck with 3000 pounds load capacity. It has the same engine as the 1/2 ton with 1500 load capacity. If I wanted to tow 9000-10,000 pounds I would need a different engine, and maybe a dual rear wheel version of the truck.