Overall should do fine.
The trans is a 4L85E 4 spd. Not the allison. Depending upon body style, may or may not have the TH mode in it.
As far as tow rating and gcwr is, These are not true legal numbers, only a warrenty and performance rating by the manufacture. More than likely you are beyond warranty. Even if this trailer was a bit more, which it is not of the manufacture limit, I would still pull it. GM probably rated this rig around 10-12K total trailer wt, with a gcwr of 16-18K lbs, maybe 20K at most. Issue is trans vs the pickups with the Allison is higher.
Just make sure the hitch setup is level from the front of the burb to the rear of the trailer. Not too much wt side to side in the trailer. Trailer is level to slight nose down. A good WD setup minimum. Some will say a sway control to a hensly....I'm saying what I would want minimum!
marty