I run a relatively light tow vehicle so I subscribe to the belt and suspenders approach, others might choose differently. Some here even choose to wear a belt and 2 sets of suspenders (mechanical sway control plus active sway control).

This is one of those topics that periodically come up because it is very important.

The perceived need for sway control is very individualistic, some people like belt and suspenders.

At 7650 pounds, do you need sway control?

From the Ford website (picked at random) -  

https://owner.ford.com/support/how-tos/exterior/trailers-towing-loading/how-to-towing-guide.html

I have to second (and third) Motor7.

I found the specs for the 2018 JKU Rubicon and assuming your 2013 is similar you have 3500 lbs max towing capacity, 350 lbs max tongue weight, and a max gross combined weight rating (MGCVWR) of 8171. The MGCVWR is often overlooked but its very important because the tow rating generally assumes that there isn't much if any weight in the tow vehicle itself. Since the Jeep curb weight is 4522 lbs, 8171-4522=3649 lbs is available for the trailer, its contents, and the contents and passengers of your Jeep. So, it looks like Jeep is rating the tow capacity with nothing in the Jeep except one skinny driver. 

The 180 official unloaded vehicle weight is 2662. That's with no options, water, or batteries, and one propane tank. Assuming you have the typical microwave, a/c, and TV it comes to 2823. There are 6 gallons (50 lbs at 8.3 lbs per gal) of water that remain in the water heater unless you drain it for winterization, a single battery is about 60 lbs, and a weigh distribution hitch adds about another 50 lbs. So call the empty trailer + wdh 3000 lbs, close enough. In reality the empty weight will be higher partly because you can't really drain all the water out of the holding tanks. My 179 actual empty weight comes in about 150 lbs higher than I get by calculation. 

So, you'll have about 500-650 lbs of total capacity left for passengers and driver, gear and tools, food and supplies, any water you want to carry in your tanks, and any mods or add ons you want to do. That's really just not enough, you'll end up over your MGCVWR. 

Also, the unloaded hitch weight on the 180 is 332 lbs, so as soon as you add a battery on the tongue you'll be exceeding the max 350 lb tongue weight spec on the Jeep.

Bottom line is that your vehicle really isn't meant for towing a trailer as heavy as your 180. Can you do it? Probably yes if you're very careful. But know that will be exceeding yoiur specs so if something bad happens you have a good chance of ending up on the wrong side of a lawsuit. Personally I wouldn't tow one of the heavy rPods with a tow vehicle with less than a 5000lb tow rating and 9500 lb MCGVWR. That's me. 

This link might help you both choose a wdh and in determining where you are relative to the max ratings of your axles, tow vehicle and trailer. 

I also suggest you actually weigh your rig so you know what you've really got. Load everything like you plan to do, including water in the fresh water tank if you're a boondocker, install the wdh, but don't tension it, that will foul up the weight measurements. Find a public scale, and weigh it adding one axle at a time to the scale. You can subtract to get the weight of each axle. Then unhitch the trailer, leave the wdh in the receiver, and weigh the tow vehicle axle by axle separately. The difference between the tow vehicle weight with and without the trailer attached is the tongue weight.  

Good luck!

So yeah, show a little mercy out there to that guy in the jeep towing the R-POD :)

We use the E2.

10-000-lb-Gtw-Pro-Series-Round-Bar-Wt-Dist-Complete-Kit-with-Sway-Control-Shank-Ball-Chains.

Priced at $265.00 online.

Doesn't look too complicated to install but thought I'd make this my first post here on the forum.

We will be towing with our 2013 JKU Rubicon.

Any advice would be appreciated.