You will probably be fine but at the upper limit. You don't have some critical information - actual unloaded axle weights, which you can probably get reasonable numbers on from Ford literature if you look hard. That will tell you how much tongue weight you can put on to the rear axle and how much cargo capacity you will have after passengers, fuel and tongue weight. Your trailer is probably going to weigh 7,000 with propane and fresh water full, and 8,000 with your camping stuff loaded (either in the trailer or in the truck bed). That puts a tongue weight around 800 - 1000 lbs, maybe 15% less with a good weight distribution hitch. All within the capacity of the truck. If it will perform to your hopes in those east coast hills with a 3.55 differential is another question, but it should be safe. I would personally invest in some high end shocks, probably Bilsteins. The stock truck suspension is pretty floaty.
Brian