Yes, that Suburban would in theory be able to tow a 7400# loaded trailer if at its 8600# limit. Something like the Keystone Passport 2910 like my family used to have would work. We used to camp in it as a family of 7.
If you can’t find a Suburban a full size van (2500/3500) would be the next best option in my opinion. Some like the Fords, I personally liked the Chevy Express. Look for a 2010 or newer to get the 6 speed transmission and additional safety features. I think around 2013-2014 they started offering backup cameras. With the GM van you could put an aftermarket hitch and not have to worry what your tongue weight is.
Best of luck with your search.
