The door sticker doesn't tell you anything about towing.
In the owner's manual, in the section on towing, is a series of charts for tow capacities. These are based on engine, transmission, body style, trim level, and axle ratio. You need these specifications to figure out the tow rating of your Trailblazer.
Shooting from the hip, you could tow a SMALL travel trailer, at most 4000lbs loaded and ready to camp. One of those 16' or shorter single axle units would work fine. My old V6 1500 pickup had a tow rating of 5000lbs, and that was generous. The limiting factor there was power; you simply could not keep up with traffic towing much.