I think that this will be too much trailer for your truck. We have a 2010 Chevy 2500 HD long bed, Duramax and the max pin weight is 3000 and max trailer weight is 13,300. Our 5th wheel weighs 12,280 loaded (no water) ready to roll and the pin weight is 2840. This setup pulls just fine, but I would not want to go any heavier.
You can find a FW that will fit within the tow limits of your GMC, but it takes some looking and you need to know your tow specs. Now I will get flamed as someone will post that they pull what you are proposing with their 2500 SRW and have no problems. Be that as it may, we prefer to stay within our limits. I'd like the truck to last us a long time.