200 miles towing an RV to a campsite is not like a quick car ride between meals.
Your issue with your current truck is payload and receiver rating. That Jayco will have something like 1200 pounds of hitch weight when loaded. Check your driver's door for as equipped payload according to the tire and loading sticker. I bet it is under 1500 pounds, maybe 1300. That number has to support the trailer tongue weight, people, and a bed full of camping gear.
3/4 ton diesel crew cab 4WD trucks don't have much payload either, say 1800-2300 pounds. Pay the extra $600 for a single rear wheel 1-ton for 800-1400 pounds more payload.