If you tow that unit with a Grand Cherokee, consider yourself on a suicide mission.
NO WAY would I tow with that vehicle.
My first TV was a 3500 GMC with 454. That was a pretty comfortable vehicle, but towing without a sway bar and WD spring bars could make for some white knuckle experiences after a new set of tires, with heavier tread depth were installed. Using a sway bar, WD hitch and a full fresh water tank, made for a much more enjoyable trip.
My current tow vehicle is a 2500HD Extended Cab, Short Bed, with Duramax/Allison. It tows it like a dream, and is more stable because of it's longer wheelbase.
Your Airstream should weigh around 6400# empty. A full size extended cab truck with V8 engine should tow it very well.