Trailer Life Tow Guides may only go back to 1999. They show the Suburban 1500 with the 6.5 engine as having a 8000 lb tow capacity but they don't show the payload capacity in that early version.
If that is the 'dry weight' of that trailer the actual loaded weight is probably at least 8000 pounds. And your Burb is 12 years older than the 99. I'd really worry about the payload, that trailer probably has at least a 1200 pound tongue weight. I suspect when you attach it to the Burb you might bottom out the rear end. We has a 94 Burb that we towed with but only lighter trailers, less than 4000 pounds. It worked great for those trailers. I would not have tried a 30 footer tho. The brakes were definitely a weak point on that car too. Pikes Peak killed the differential on it too, on the way down.
Yes to the WDH if it seems that it will tow that trailer