Hello Brox, Fellow Jeepster.
I, too, tow with a Liberty. But, we are comparing apples to oranges, because I have the diesel. I took my unit by the CAT scales, full of water, with the family, on my way to a campground. Granted, I only had the water full for weighing, and I never travel full of water. Anyways, I was 100lbs over GVW on the Jeep and I was 4400 on trailer if I recall.
Anyways, get the BEST WDH you can. Either the Equal-i-zer 4p or the Reese Dual Cam straightline. You will need it. I rented a 24 foot Amerilite before buying the Roo, and with a cheapo WDH, I was not a happy camper.
Another thing, change the tires. I am running P rated Hankook Dynapro ATM in 245/70R16 XL rated. But, if I was to do it again, I would get with LT245/70R16 in either Cooper Discover AT3 or Falken Wild Peaks.
If you are travelling flat, you should be able to do it. If you start doing hills, you will struggle. I have loads more power in my 2.8 diesel with the Green Diesel tune than you have in your 3.7. Best of luck. Any questions, feel free to PM me.