Welcome to the Forums and the world of Airstreaming!
What you are looking for is something that is required with most pickups/sport utilities used to tow an Airstream. I have towed my Overlander with a Jeep Grand Wagoneer (1984 - pre-downsizing), a K1500 Chevrolet Club Cab Pickup, and my current K2500 GMC Suburban - - each required the use of a drop hitch very similar to the one pictured below (it is installed on my Suburban):
The draw bar/ball mount pictured above is for my Reese Straight Line Hitch, but similar dropped ball mounts are available from most of the major manufacturers. Getting a hitch that is properly rated for the weight involved with the proper weight distribution bars and sway control is also something to be considered.
You are correct in assuming that it is important to get the trailer level for towing. It can be quite expensive to drag the rear of the trailer on the ground as the dump valves and related plumbing can be rather easily damaged on the rear bath coaches. The coach will also handle better if it is towed in a near level state rather than nose high.
Good luck with your search for the ideal tow vehicle!