Personally, I wouldn't even consider it. You'll have plenty of power, but the coil springs, the low GVWR (6600#), and especially the short wheelbase (119") make it a poor towing platform for a trailer that large.
FWIW I had a 2000 Durango, which I traded in for a 2003 Ram 1500 when I got my Kiwi 23B (23' hybrid) because the Durango wasn't up to the task. I realize the 2004 Durango is a slightly different animal, but so is that trailer, by a lot. My current trailer is about the same size as that Coachmen, but even though my Ram was a 4x2 (which has 400# more payload than a 4x4), I was still over my GVWR by about 100#.
I now have the truck in my sig, which has GVWR=7650# and wheelbase=144". It's an excellent combination, but I wouldn't want to go with much more trailer or any less truck. And I especially wouldn't give up 2 feet of wheelbase.
-- Rob
2013 F-150 SCREW 4x4, 3.5L Ecoboost, 3.73, 7650# GVWR, 1826# payload
2004 Springdale 295BHL, 31'5", 7300# loaded
Hensley hitch