To the OP. It won’t win any races, but it will pull that trailer safely and reliably (provide the burb is in good shape of course ).
We have a fleet of mostly 2008 6.0 Chevy 2500 and 3500 trucks. They’re construction trucks so care and maintenance leaves a bit to be desired.
Haul trailers that heavy or heavier all the time with them.
Sent 1 over the pass yesterday. Trailer was probably around 12klbs. Guessing. It easily was well over 10k. Came back hooked same trailer to a different 08 and back over with another load.
For the Op, 4 speed and 3.73s isn’t the “best” 6.0 towing setup but it’ll dooo. That 6.0 will scream at whatever rpms you need to get where you’re going for many miles!