Maybe she updated her original post after everyone read it but the first post clearly said they have already put on a weight distribution hitch AND anti- sway, and adding a brake controller.
Looking at some on-line specs. Trailer weighs 7700. Suburban can tow 8100. If that trailer is totally unloaded, no propane tanks, no battery, no personal items, etc, this looks like it is doable. But brake hookup, weight distribution, and anti-sway must be be in place, as they already are.
BTW, as most of us know a brake controller is mandatory by law!!!!