Yep. Gross combined weight rating is 15,000 pounds for this vehicle so you have nearly 8,000 pounds left over for the trailer.
I use the Equalizer 10,000/1000 pound WDH as tongue weight runs over 700 pounds from time to time. Once setup it's set up. Turn the air suspension OFF when setting up the WDH and measure carefully. The front suspension must compress or no weight transfer is occurring. Air suspension can go back on when done to get the last 1/4" out of being level.
As you get closer I can give you my Equalizer settings which will probably require no adjustment for your trailer since we have the same truck (although mine is an XLT specifically to avoid the air suspension!).
-- Chuck