Yeah, trucks don't carry weight determined by its GVWR number.
Fords 2500 has a 6100 RAWR determined by the lessor of tires/wheels or rear spring pack ratings.
Fords F350 SRW has a 6290 RAWR determined by the lessor of 17" tires/wheels ratings. And several GVWR numbers.
Fords F350 SRW can have a 6730 or a 7000 RAWR determined by 18" or 20" tires and wheel ratings. Also in several GVWR numbers
And Ford makes a F350 SRW with a 10000 GVWR or a 11200 GVWR in the same exact truck ie;
a crew cab 172" wheelbase 6.7 diesel 4x4 6290 RAWR 17" tires and wheels.
Ford markets F350 SRW trucks with about a dozen different GVWRs from 10000 up to 11500 GVWR in 100-200 lb increments.
The F250 can be ordered with the heavy service package which is same package as the F350 SRW.
You sure don't need a one ton DRW trucks for that size trailer.
Use this spec sheets from Ford for all the mechanical specs for the F250/F350 SRW trucks from '00 up to 2016 models. Separates internet misinformation from Fords facts. https://www.fleet.ford.com/truckbbas.../techspec.html