I tow a 1963
Tradewind (24') single axle with a 2007 Jeep Grand Cherokee diesel. I us an Equal-i-zer sway control hitch. The Tradewind weighs 4400 lbs. fully loaded, so it is lighter than newer Airstreams.
I am very satisfied with this match up. Pleanty of power. Good mileage (18mpg). Very comfortable ride. AND... the backup camera allows me to hook up unassisted.
MTW.... my Dad towed a 1962
Overlander (26') all over North America with a Jeep Wagoneer. He haver had a problem. BTW, that was before traction control, and he used an EZ Lift hitch without any sway control.
I think you will be very happy with the Jeep if you don't buy an Airstream that significantly outweighs the Jeep.