The maximum trailer hitch weight capacity is less than the rating on the hitch receiver. The manual states 1200lbs max tongue weight most likely due to the P tires, coil springs and drive train limitations. The TT will most likely be at or over 8000lbs with a tongue weight of 1100 to 1300lbs. You're in 3/4 ton territory. That 5.3L is going to hate you for longer trips. I'm not saying you can't do this. I'm saying it'll be a struggle. I wouldn't try the cross country trip with this combo thru mountains.
Link to manual. page 4-53
The manual also states:
8800lb towing for the 4.10 axle ratio
7800lb for 3.73
6900lb for 3.42.
These are all things I considered and researched before buying my 3/4 ton Suburban.
By the way, the GM hitches of that generation truck are junk. Replace it with a Curt class V for a couple hundred bucks. Mine bolted on in under 20 minutes.
