This is a bit of a guess, but the first question is to ask the truck rental company if they have any restrictions on what you can tow.
Second, you will need a brake controller installed, is your rental company OK with that?
Third: You may not need a WD hitch for the tongue weight, but sway control can still be an issue with a big trailer. I assume it is a 31' or larger trailer?
Forth: If you do not use a WD hitch, but only a simple ball mount stinger type, be absolutely sure that it has enough capacity for the load. Many of the inexpensive ones are just for small trailers, not the weight of an Airstream, tongue and total load.