A few of your numbers are off a touch. Unfortunately the spec section on the Chevy website is abysmal for these purposes.
The new Chevy Dually 4x4 will have less than 7442# payload - a crew cab Dmax dually 4x4 weights north of 8000# - possibly closer to 8800# if memory serves and the GVWR is 14,000# so 6k at best, probably closer to 5k net.
The rear axle at curb will be more than that, likely a bit above 4k. The Duramax is heavy up front but the 8k ish curb weight is somewhat split evenly due to the wheelbase.
Rear GAWR on the Dually is ~10,400# so you have quite a bit of headroom
The dually truck will have a GCWR of at least 40k with the diesel. As far as carrying capability - truck at 14k GVWR + trailer at 19k GVWR gives you 33k to play with, provided you don't overload the truck rear axle.
EDIT: take a look at the specs in this link - much more in depth than the standard Chevy website, corroborates most of what I pulled from memory above.
www.gmfleetorderguide.com