Not familiar with eth Suburban, but my daughters family tows a slightly larger Jayco 28BHBE, gross weight 9200 lbs, with a Ford Expedition. What makes it viable is that it has the factory installed HD Trailer Tow Option which includes a bigger radiator, transmission cooler, higher rear axle ratio and electric brake controller.
If your Suburban has all of that, I would not be concerned.
Last tip. Know your load. Take the loaded Suburban to the scales and have it weighed. Same with the trailer.
The kids will love it.
Your only other choice is a 4 door 3/4 pickup. Pretty cozy in the back with 3 kids and a dog.