My trailer is less than 6k dry but is close to 8k loaded. One reason I have decided to stay with my 2003 Suburban is that the 2007+ versions can only handle 1000 max tongue weight. My trailer tongue is in the 1200-1300 lb range anytime I have weighed it.
Mine is a 2500 model and it tows nicely. Very stable. I would be willing to give it a try with a 1500 model, but I would likely go over GVWR and rear axle ratings. It makes sense to target a lighter trailer. Maybe a loaded weight of 6500 which should keep your tongue weight under 1,000 lbs.