The Unlimited is listed at 4,521 lbs. The payload capacity for the unit you are looking at from my quick look up is 4,527 lbs. so that leaves you 6 lbs. of spare weight, that's assuming you load noting else. I'd double check your numbers but from what I'm looking at you don't have enough to safely tow your Unlimited inside the trailer. Most Wrangler Unlimited Jeeps are toad behind motorhomes.
I do see some guys with 4 door Wranglers but they are usually on something like an flat bed trailer with an trailer or pop up mounted to the flatbed.
