Fifth Wheel Capabilities Truck

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.pdf

According 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.

Looking at GM online fleet ordering guide CLICKY LINK shows your 2500 Chevy WT has 3500-3600 lbs payload. The truck will have no problems carrying that trailers pin weight.

Now the deal killer is GM say the '12 2500 WT 6.0 4x4 short bed 3.73 has a 9800 lb tow rating (4.10 gears = 14300 lb)

IMO any smallblock pulling over 12k will not make for a comfortable towing experience. The truck will struggle at those loads. I would stick with a 10k wet weight trailer.

I would say your ideal fifth wheel trailer length would be 29 to 30 ft.

Maybe yes, maybe no.

It all depends on how much the "10,500lb dry weight fifth wheel" REALLY weighs loaded and ready to camp.

It all depends on how much payload your truck has left.

10,500lbs is going to be 12,000lbs by the time you're loaded for camping. That's an awful lot behind a 6.0L gasoline engine even considering the 6-speed transmission.

Your pin weight is going to be in the 2400-3000lb range, plus 250lb for the hitch in the truck. That will max out the stock rear tires on the truck, and it will likely require airbags or helper springs. It will almost certainly be over the GVWR of the truck.

Even not knowing the exact weight of your truck and the payload it has left, a 10,500lb dry 5th wheel is going to pretty much be at the truck's limits, and your limits in the patience department as well.

You will probably be close to the limit by the time you add water, clothes, food, propane, etc. Say you add 1k lbs. of weight, that will put you at 11500, witha pin weight around 2200 lbs. That would probably bee close to you payload limit, though I'm not sure. You get the idea though. Also, dry weight doesn't account for add ons, such as ac, awnings, etc., so you're more than likely already heavier.

YES!!!!
With your configuration there is no way you would be comfortable towing any more than 10,000 pounds GVWR.