I agree with above. Check the Ford Fleet link someone posted above. In the year you specified the payload is 2400-2500 depending on short bed/long bed for crew cab. The same year F350 has about 1000+ more capacity in payload so as others say it would be prudent in upgrading rear suspension.
I did tow 5th wheels with a 2014 F250 XLT and it had plenty of power but did sag on the big ones (15k GVWR). It was a work truck and my only option so I dealt with it. I was solo (min cargo) and the trailers were empty with no cargo, propane or liquids (new) so I was on the lighter side. Add family, luggage, food, liquids and propane and things would change.