I agree with Bob & Patty,
My last truck was a 04 2500 Dodge Cummins 4X4 Quad Cab with all the extra towing stuff...very simlar to your GM truck.
My new trailer is Cyclone 4012...not much more than the 3712. Right off the bat the 3712 is about 12K pounds dry...that's just about your max already witha 3/4 ton truck.
I bit the bullet and bought an 08 Ford F350 Crew Cab 4x4, DUELLY with the 13K truck GVWR ( the highest made). Still, the most I can legaly tow is 17800. My trailer has a GCWR of 18000. So, technically I'm illegal. Yes, I don't plan on carrying motorcycles and such so I will probably really be at 16-17K at the very most. But, the CHP don't care about that. They look at the actual ratings. And, if I get in a wreck...I'm positive the police and/or my insurance will be looking very closely at my weight ratings. I can live with 200 pounds, but not with 2000+
The 3/4 ton truck will be way under rated...even with airbags, tires, etc. And, if my 1 ton barely, if at all, makes it, what do you think the 3/4 ton will be?
The question you should NOT be asking is "can I carry that trailer?"
The question should be "should I carry that trailer?"
I drive big commercial trucks (fire engines and fire trucks) for a living and I see folks in F-250s and 2500 trucks towing trailers that are obviously too big rather frequently. I would not go as far as calling them organ donors, but I will say the bring a good amount of business our way. I mean no disrespect here...these are just the facts.
Good Luck in whatever trailer you chose. If it is a Cyclone or Razor, I know you'll be happy with it.
Rock On....