There is a serial number attached to a metal plaque on your trailer. Take a look at Airstream.com's FAQ page
and you may be able to confirm the trailers identity. Or else ask back on this thread and let some experienced heads help you decode it.
It may be in better actual condition if it was stored inside. Your father sounds like he'd have kept after window seals, etc. Dads are tough to lose -- I lost mine four years ago and have come up with many, many questions as I go over his old photo albums, etc. My heart goes out to your family!