I can't find towing specs for your truck so I'll use the 2004 F-250 CrewCab diesel 4x4. Specs should be similar.:
GCWR = 20,000 pounds
GVWR = 8,800 pounds.
So that means the maximum combined weight of truck and trailer is 20,000 pounds and the maximum weight (including hitch weight) on the four truck tires is 8,800 pounds
My F-250 CrewCab diesel 4x2 exceeded the GVWR of the F-250 with my 5er that grossed 8,000 pounds. And that was just me and DW and puppydog in the cab. I hauled a coupla hundred pounds of toolbox, and had a Rhino spray-in bedliner that added some weight. Without the toolbox or bed liner, I probably wouldn't have been overloaded.
Your 4x4 adds about 400 pounds of weight to your tow vehicle, and your shorty bed subtracts about 200 pounds, or net of 200 pounds of weight from the max hitch weight you can tow without being overloaded. So with your truck I'd look for a 5er with GVWR not more than 6,000 pounds. Those are few and far between, so I'd probably opt for a TT instead of a 5er until I could afford more truck. With a TT you could consider one with GVWR around 7,000 pounds, then with careful loading you may not be overloaded over the GVWR of your truck.
To get a more exact answer, load your 2500 with all the people, pets, tools, hitch, camping stuff, etc. that will be in it when towing. Go to a truck stop that has a CAT scale and fill up with fuel. Then weigh the wet and loaded truck (including driver). Subtract the weight of the truck from the GVWR and the answer is the max hitch weight you can have without being overloaded. Divide that available payload capacity for hitch weight by 17% and the answer is very close to the max weight of any 5er you can tow without being overloaded. Divide that available payload capacity for hitch weight by 13% and the answer is very close to the max weight of any TT you can tow without being overloaded.
Grumpy ole man with over 50 years towing experience. Now my heaviest trailer is a 7,000-pound enclosed cargo trailer, RV is a 5,600 pound Skyline Nomad Joey 196S, and my tow vehicle is a 2012 F-150 EcoBoost SuperCrew.