While the 2500 (3/4T) would be a better towing rig, your 1500 'Burb should be OK for the job IF it has the towing package with 3.73 gears. Check for a label in your glovebox that lists equipment codes.
GU4 = Rear Axle: 3.08 Ratio
GU6 = Rear Axle: 3.42 Ratio
GT4 = Rear Axle: 3.73 Ratio
The 3.42 axle is IFFY for towing a 28' trailer and the 3.08 gearing on the 1500 just ain't gonna cut it. Basically the lower the number, the harder the engine and transmission have to work to pull a load.
I concur on the added cooling for the transmission as well.
1995 Coachmen Santara 360MB 36' w/slide.
Ford F53/460 chassis, 1997 Jeep Grand Cherokee "toad"