Hi Narnian and welcome to the Airstream site!
I would have to concur with the replies regarding adding AC, as opposed to hoping to find another trailer with all you want AND functioning AC.
In the price range that you are considering, chances are that you will be looking at late 60's to very early 80's models.
At that age, many of the air units are not operating or near a point of exhaustion. Plus, some of the late 60's-early 70's models used air units that are no longer being produced (ie: Armstrong) and repair parts are next to impossible to find. So if there's a failure you may have to replace the air conditioner anyway.
So, if all else seems above-board and you like the features (such as single axel, floorplan, etc.) of this trailer, I wouldn't let the need to add AC hold you back.
On the other hand, you may feel more comfortable in your selection after you've had some time to look around at other Airstreams for sale. This might give you a more complete picture of what's available at various price points.
'Just my $0.02