I would need a bit more information to be 100% sure but on first glance I think you are good.. HOWEVER do not take my word for it.
Here is where you need to be to find out:
Trailer Life 1999 towing guideFrom the looks of it, depending on just exactly which of the Suburan line you have.. You may be well within tow ratings.
As for the "Get the biggest truck you can" crowd (of which I am part) I usually send folks to
http://www.trail-hauler.com which is the site for folks to shop if they do not wish to ever ask the question "Can I Tow That". But the fact is the bigger the tow vehicle, the better the tow vehicle, That is, the less you will feel the towed, and the easier it will be to handle..
But the chart I linked to should give you the facts regarding YOUR truck. Being as its a '99... I'd try to give it a bit of Headroom, say take a thousand pounds or 20 percent off the tow rating of the truck.