I'm not 100% sure of the tow ratings on that truck so, it is hard to say for scertain. A quick google search turns up a 4.7 v8 in that truck and a 7200lb tow rating. If both of those are true, then you should be ok. I would advise a weight distribution set up and anti-sway though.
My previous TV for my X-250BHS was an '05 F-150. The 5.4 V8 had plenty of power to pull that trailer. It was working pretty hard those in quite a few instances where i was climbing a steep pass here in Oregon. I was never the guy holding up traffic though. With a 4.7 you will get up those hills, but you might need a bit longer to do it.
I also found that even with a weight dist. set up my TT did bounce and push my truck around quite a bit when i was fully loaded. There was never any danger just pushing near the limits of what a 1/2 ton truck should be towing, imo. I generally take a lot of gear with us when we go so my weight is up there.
'09 F-350 6.4l Crew Cab
'10 Komfort Trailblazer T262BSLE