As stated, your numbers look good.
A trip to the CAT scales with your loaded rig will confirm theory.
Weigh the truck, weigh the truck and TT, you will get the front, rear, and TT axle weights.
Then you can calculate the actual numbers.
As to how many horse power you need, only you can tell if the combination is under powered. My little 200 hp. F-150 had a heck of a time with a 6000 lb. TT in the Ozarks. It wanted to down shift all the time. I upgraded to a 356 hp. E-boost and it pulls fine for me even in the Rockies.
Good Luck
