http://www.chevrolet.com/content/dam/Chevrolet/northamerica/usa/nscwebsite/en/Home/Vehicles/SUVs%20and%20Crossovers/2012%20Suburban%20Three%20Quarter%20Ton/Model%20Overview/02_PDFs/2012_Suburban_3.4_Trailering_Guide.pdfAccording to Chevy's site you can only tow 9500lbs. The killer is the 3.73's. If you had the 4'10's you'd be good for 14,000 in a 5'er. 9500lbs isn't much but there's still quite a few 5'ers in the "1/2 Ton" style that would work well. Something with a dry weight around 8000lbs or even less would get you something decent. I couldn't find the payload info for 2012 but for 2013, your truck starts at 3189lbs. so assuming they didn't jump the payload numbers too much if any you have plenty of payload for the 9500lb limit.
Check your door sticker for CCC.