Tow capacity, Electric brake box inside truck,tranny cooler?

Being as OP has not said WHICH of the models he has, he may very well have the 8300 gvw 150. Which in reality, could handle a 13k trailer...
If he has the typical 6600-7200 gvwr optioned 150. 13k is out the door.
The 3.5 turbo does have the power to run down the road at 18k lbs or so total

As far as a brake controller. Been very happy with the prodigy the last 20-25 yrs or so it's been out. I've had 3-5 of them in different trucks, replaced due to age etc

Marty