Unfortunately, not enough info. You really need the the trailers GVW. You can easily ad 1-2k in weight once you add water, propane, food, dishes, etc.
No matter what you get you will need a weight distribution hitch, which will help a bit on the weight you put on the truck, as it spreads it out to both axles. With this one, you MIGHT be able to get away with the F150, although don't expect to be able to haul the quads.

 

Err...you're thinking about doing this to avoid staying in a hotel?

Unless your family simply has an issue with hotels, I do not see how this will be a benefit. Your fuel milege will plummet. You will have to deal with towing a trailer everywhere you go...probably more trouble than you are giving credit. If you can comfortably drive 8 hours, expect to be exhausted after driving only 6 hours with a trailer behind you. It jerks the truck around, acceleration goes to crap, stopping distance increases dramatically, and contrary to what some people claim, you never, ever actually forget it is back there.

With the decreased fuel milege and the roughly $40/night site cost at a KOA campground I fail to see how this is cost or comfort effective with regards to travelling.

On the other hand, if what you want is something to tow to the local campground and spend a long weekend with the wife and kids fishing and sitting around a campfire a few weekends a summer, I strongly recommend a camper.

Just my two cents,
Mike

 

I have trailered many Mustangs, and full size trucks around, so I know the issues. I just never, and I mean never, gave weight a thought.lol Everywhere around here, or at least the places I stay at. They jack their prices way up on the weekends we are going on vacation. But, the jack them up higher than their normal increases sometimes. Plus, we would use it for the dunes, up north, going to NMRA drag race events. That's the biggie, I'll be racing my car, and want to be able to relax as much as possible between classes. Hence, my own place, for whatever you know. Plus, I've always wanted one, and it was my wifes idea this time.

 

Why not a toy hauler? Almost any RV you find will put you over GVWR of your truck with two qauds in the bed and a family of 5. Starcraft has a few models that I've always been interested in for camping with family and quads. The 18SD and 21SD will hold two quads I nthe front while the 19SD will hold one on the front of the trailer plus one in your truck bed.

Anything you tow over about 4000 pounds will benefit from a WD hitch.

 

I don't know what your budget is (as these are pricey).
Fuel costs have me considering Trailmanor. http://www.trailmanor.com/
I'd go with the big double axle 33xx King, sleeps five.

A 33 foot trailer @ 3500 lbs and no wind resistance is looking pretty good to me.