Make sure you measure the height of the rig when it is hooked up to YOUR truck. They can publish any number they want, but it will not be the same when you're hooked up.
The published number is the highest point with the installed components, which is usually a rear AC. If you add a front AC, the height will likely be higher. I installed a Dometic Penguin low profile unit on mine, and it saved me several inches. My hitched height is 12'-10".
The way I measured was to hook up and park on flat and level ground. Then I took a straight 2x4 and set one end on the highest point which is my front AC. Next, I placed a level on the 2x4 and held it level. My DW ran a tape measure to the bottom of the 2x4 where it extended past the FW, and measured to the ground. I made a label and attached it to the TPMS monitor so I can see it any time I need a reminder of the height. Just remember, that bumps, hills, and your load can change the height, so make sure you don't cut it too close.