Specs from a Chevy website, for 2015 Suburban
2WD
payload 1682 Max tow capacity 8300
4WD
payload 1643 Max tow capacity 8000
Average weights, percentages, and items to keep in mind when doing your calculations:
1. Every pound of people, aftermarket accessories, cargo, weight distribution hitch, etc, that you put in, or on the tow vehicle, takes a pound away from payload and tow capacity.
2. Brochure weights are notoriously incorrect and not normally in your favor. The trailer most likely, is heavier. A dealer could have two trailers of the same model, with different weights. Your model for example, at several online advertisements, the UVW varries by as much as 400 lbs.
3. Before the trailer leaves the dealer lot, it will gain weight from propane, battery, and any dealer installed options. The biggest gain will be tongue weight.
4. Average trailer load of dishes, pots and pans, utensils, bedding, camp chairs, BBQ equipment, groceries, toys, bicycles, and water, etc, weighs 800 - 1200 lbs.
5. Average tongue weight is about 12.5 percent of loaded trailer weight. Actual tongue weight will go up and down during every trip. Groceries and water get used up. Black and grey tanks get filled.
6. Holding tanks can have a huge impact on tongue weight. Depending on their location, in relation to the trailer axles, they can make tongue weight go up and down quite a bit. (My fresh tank has a 150 lb, up and down affect on my tongue weight)
7. First camping trip will be lower weight than any future trips. That's when you find all the things you don't have onboard. If you're on the edge (weight wise) out the gate, you're probably going to go over.
When loaded for camping, looks like that trailer will need about 800 lbs of payload.
Unless you go crazy with loading stuff, you should be OK.