You have to look at the Gross Axle Weight Rating (GAWR) of the F150 you are considering. You can find that on a sticker inside the driver's door. Then, you have to know the actual weight that each of the truck's axles is supporting when it is "empty" - just you in the truck with full gas and other fluids but nothing else. You CANNOT trust the listed or advertised weight ratings for this. You have to take the truck to a CAT scale or other "certified" scale and measure the weights on each axle.
Then, you add in the weight of the tongue of the trailer you are considering. That weight is being supported by each of your truck's axles. Add in the Weight Distributing Hitch (WDH) you are considering too - mine is 70#. Add any passenger's weights you are planning to take with you. Add the weight of all your camping gear that you are planning to put in the truck. If you are filling the fresh water tank in the trailer, it will add at least 100# to the tongue weight.
If you do all this, you will discover that you have weights on each of the truck's axles that exceed the GAWR of the truck. There is a reason that F150s are classified as 1/2 ton (1000#) pickups! Yes, you can overload that truck for short trips - I do it all the time, hauling concrete, or at times, trash to the landfill. But, you do NOT want to do this on a long camping trip.
An F250 should be able to handle that trailer, but not an F150. I have a cap on the bed of my pickup, and with its weight, I can only add about 700# to the "empty" weight of my truck, if I want to stay under the GAWR.
As I said before, that truck will easily "pull" a 10,000# trailer. It just won't safely support the additional weight on the axles.
- Jack