2012 Towing Specifications with Vehicle Loading Calculations:
First off, I am going to use your assumed tongue weight in my conclusion below. However it is a good idea to check your Tongue weight as I have personally owned a 19' Ultra Lite and with water the Tongue tipped the scales over 800 pounds and the trailer weighed under 5000 loaded due to the water tank location. This is something I learned from in my 3rd trailer in watching water tank location as having water that far forward made for some negative handling performance in the trailer. My current trailer has the water tank directly over the wheels and I often go dry camping or hydro only so to some people this is important.
2012 V6 Towing Capacity 5000 Pounds (When equipped with a factory tow package)
Tongue weight capacity with a WD Hitch - 750 Pounds (500 Pounds dead)
GVWR of the Vehicle: 6500
Curb Weight: 4470 (depending on options)
Payload: 2030 (approximate)
Calculated Payload with Trailer at Maximum Tongue weight: 1280 Pounds
4 Adults @ 225 Pounds per person would still leave 380 Pounds payload capacity.
As the trailers you are looking at would likely be lower tongue weights you have a fairly comfortable margin there. The only thing I recommend is getting your tongue weight and trailer weight checked loaded at the Scales after you have everything set up. It may change how you load your trailer as this can have a significant impact on the handling of it.
Shurline makes a tongue weight scale if you are interested, it was the tool that was the real eye opener to me.
Sherline Trailer Tongue Weight Scales
Jeep Grand Cherokee is an Extremely solid towing platform... In the current V8 platform it is actually rated up to 7700 Pounds in Australia to give you an idea of the body resilience. It is only rated for 7400/7200 (4x2/4x4) here in a V8 but these are all on the same Chasis as your current vehicle. I consider them to be one of the most pleasurable towing vehicles around!
Let me know if you have any other questions.