It all depends on your driving style, and how fast you want to get to the top of the hill.

Back in the 60s and early 70s a friend pulled a two axle Monitor travel trailer all over the country with a 55 or 56 F100. Totaly stock with many miles on it. It had a 3 speed. In the 80s someone else I know regularly pulled trailers upto 10,000 lbs with a 77 F150, 300 six, 3 speed automatic hauling grain and feed.

Both did it at a steady pace, taking things as the truck would.

Your truck will pull a 2000 lb travel trailer if both are set up properly. Good trailer brakes on the trailer, possibly a weight distributing hitch (not usually necessary, but it may make things handle better). Go over the brakes, shocks and springs to get all in tip top condition. You will not be the fastest on the road, but you will get where you are going and have a reasonable cruising speed. These trucks were built to move a load, and in good condition the engine, clutch, transmission, cooling system, brakes, and axles will be up to the job. The biggest thing is that your driving style and expectations must match the performance of the vehicle.