I'm going to get a reputation for being a nay-sayer around here...
Your truck isn't designed to tow more than a utility trailer as it is right now... The F150 is a fairly heavy truck and the V6 was designed more for urban cowboys carrying mulch and sporting equipment. Sorry...
Even with the tow package, that would include at a minimum, a transmission cooler and heavy duty alternator, at 5400 lbs max, the trailer you are looking at would be a bad idea. The trailer has a "dry" weight of 3995 lbs. By the time you add "options", LPG and a battery, you are probably looking at a "tow it home empty" weight of ~4200 lbs. It won't take any time at all before you exceed the max tow capacity of your truck by the time you add "stuff" to the TT to make it livable and the weight of weight distribution hitch has to go in there, too. It is a toy-hauler to boot...you won't be able to take any toys unless they are a couple of bicycles.
Then you have to figure the "sail area" of the TT...the V6, while capable of towing a utility trailer that doesn't have any frontal area to create drag, is not up to overcoming the wind resistance of a full sized RV trailer and you certainly won't like hills.
All the above is not to say that you can't have a frame mounted hitch installed, a transmission cooler added, a heavy duty alternator added and the appropriate 7 pin wiring installed and then tow the mostly empty trailer around, but, it will be expensive, drastically shorten the life of your truck and won't be a whole lot of fun. I'm not one of those folks that think you need a 3/4 ton diesel minimum to tow with (I tow with a Jeep Commander), but, I think you do need more truck than what you've got, for that particular trailer.
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