Your looking at a 10500 GVWR trailer which any F250 diesel out here will handle that size trailers hitch weight with ease. And of course it will have no problems pulling that small size 5th wheel trailer.
Ford give's the F250 a 6100 RAWR. A 3/4 ton diesel truck rear axle may weigh in the 3000 lb range which leaves over 3000 lb for a payload.
The F250 with the "heavy service package" with 18"/20" wheels and tires has the same specs as a F350 SRW. A good Ford truck dealer can fill you in on how to's.
If you decide to go with a F350 SRW be sure it has the higher 11.2k- 11.5k GVWR and 7000 RAWR.
Ford markets a 10000 GVWR diesel F350 SRW which gains nothing over the F250 diesel with that heavy service package.