Before spending money on a different truck, I'd say to figure out why the current rig is giving you handling problems.
1. Look at the truck's payload and other ratings, and figure if you are overloaded or not. Have you weighed your trailer tongue when you are loaded for camping?
2. If not overloaded, is the tongue weight inappropriate? It should be 10% to 15% of total trailer weight.
3. If hitch weight is ok, how long is the trailer? And are you using any anti-sway device? If not, trying a WD hitch with built in sway control is much cheaper than another truck.
4. Are you running LT tires or P tires on the truck? If the latter, switching to LT tires with a shorter sidewall could help alleviate the problem.
There may be other things to look at and try besides these, but you get the idea.
Mike G.
Liberty is meaningless where the right to utter one's thoughts and opinions has ceased to exist. That, of all rights, is the dread of tyrants. --Frederick Douglass
photo: Yosemite Valley view from Taft Point