For what its worth, my girlfriend's truck is an F250, similar construction to yours, rated for 18K#.
My F350 is rated for 21K#, but I am limited to 18K as well, due to USDOT regs.
If I scale over 26K, I am required by law to have a CDL, because my truck has commercial signage as well as being owned by a business. Makes things a little fuzzy, but that's what the DMV told me.
A 2000# trailer plus a 1000# horse, gear, etc, on a 3/4 ton is a walk in the park.
I would, however, be concerned with tongue weight. Load it too much forward, and you'll have problems.
Load it too far back, and you'll get wag, which can be lethal.
I have both gooseneck and bumper pull hitches on my truck.
I use the goose whenever I can, as I find it easier to maneuver in tight quarters, and it tends to ride better in general, with the bulk of the weight distributed onto the rear axle makes for a smooth ride.
I RIDE, THEREFORE I AM
COWBOY UP OR GO CRY IN THE TRUCK