I think that you will do fine. Just make sure that you are not picking up 'any F-150 on the lot' - you need to select one with all the heavy duty towing options.
If you just walk in and pick a F-150 EB truck, you probably will get a light GVWR. If you select the correct option package, you can get a 7,800 pound GVWR. There is a HUGE difference in the two trucks. One will have about 400 pounds extra cargo rating, while a standard pickup ordered as a grocery getter will not have nearly as much GVWR as you might need while towing.
Good luck,
Fred.