I've pulled with a 2011 Ram 1500 with 3.92s and while the truck could pull the load, she was maxed on payload and squated pretty good in the rear. Your truck has more than enough power to do the job but with 3.55s, man that thing is going to struggle. Gas milage will be somewhere around 6 or 7 mpg if I had to guess and she'll be screaming up hills. Watch your tranny temps and oil temps as well.
I'd say honestly, you need a bigger truck or a different truck with better gears (and integrate brake controller since the trailers you are looking at are rather large). That truck will struggle and I'm a huge Ram fan!
I traded mine after pulling rentals the last few years...weight was from 4K to 6K on the rentals and gas milage on the higher ones was 7 or 8 mpg. Best i ever got was on a 19 footer and averaged just a shade over 10 mpg. The truck was full tow package, brake controller, 5.7 Hemi, 3.92 rear and she would squat pretty good. Laramie too with Ram boxes so my payload was roughly 1,036 pounds!
I'd suggest a smaller trailer or a bigger/different truck..more so based on the fact you said FAMILY. If it was just you...sure, you might pull it off but adding gear and food for 4, no way.
2014 Ram 2500 Laramie, 4X4 CC, 6.4 Hemi, 3.73
2015 Jayco White Hawk 28DSBH Summit Edition