Welcome to JOF
My 2002 2500HD 6.0L/4.10 tows my loaded 8,400lb TT just fine on the flats and hills, but the 6.0L will scream a little like most Vortec's do when under load in the mountains.... but gets the job done, and your 6-speed tranny will work to your advantage over my 4-speed.
If your into watching your TV's weight limits ........, you may find reaching your 2500HD's GCWR with a 10,000lb loaded FW very realistic...., but your loaded pin weight should be fine with the 2500HD's payload capacity (figuring 20% of FW loaded weight).
Travel safe and enjoy your FW.
Bob
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2016 GM 2500HD 6.0L/4.10
2018 Jay Flight 24RBS
2002 GM 2500HD 6.0L/4:10 (retired)
2005 Jayco Eagle 278FBS (retired)
1999 Jayco Eagle 246FB (retired)
Reese HP Dual Cam (Strait-Line)