Ah, the weight police have shown up early. Many here believe that unless you have a 3/4 ton (diesel preferred) you shouldn't tow anything larger than a pop up. You have come to the right place to get answers but be prepared for all sorts of answers.
OK, the limiting thing with half ton pickups is their limited payload capacity. You do have to watch the GVWR numbers and this is the big thing. My Tundra has someting like a 1700 pound payload rating. Once I drop the trailer on the hitch I have something like 700 pounds left to take care of me, the wife,a generator and some lawn chairs.
Half tons make good tow vehicles but you do have to watch the weight of your trailer and the tongue weights. Don't look at dry weight numbers, look at gross vehicle weight numbers. They usually post 10-15% of these numbers at tongue weights even though the are usually higher. Salespeople are probably the worst to get honest answers. I suggest that you go on the trailer website and ask owners what their numbers are. If you are interested in a particular kind of Jayco, go to the Jayco site, or this one for that matter, and ask specifically about that trailer. You will find that many will be towing with your kind of truck.
Good luck. It is late in the season so I am assuming you have just started to look. Take your time.