The max tongue weight you can have on a 2014 F-150 is 1130 pound as per Ford's 2014 towing guide. So with that trailer, you'd be way over. So ya, the back end is going to drop. Not to mention that you need to check your allowed payload on the yellow sticker inside the driver's door.
Glad to hear you can get a new trailer or a new truck. Both our RV salesman and our Ford salesman told us we could tow much more and tried to sell us bigger trailers and trucks without the Max Tow package (which we needed). And we ended up buying a trailer that was 5500# loaded with a 775# tongue weight and we are close to our limits for payload and rear axle weight rating on our truck.
I bet I could do the 11,200 pounds my truck is rated for if all I was doing was using chains to haul a cargo truck out of the ditch. Other than that, my max tow rating is useless to me. ;)