I just bought an old 1960's airline acoustic off ebay.
http://cgi.ebay.com/Vint-1950s-60s-Airline-Acoustic-Guitar-Great-Cond_W0QQitemZ150300527024QQcmdZ
How difficult is it going to be to convert this to a lefty guitar? Do I just have to remove the nut and switch it around?
One chord is fine.
Two you're pushing it.
Three and you're into jazz.
Congrats
You'll probably need to replace the nut with a newly cut lefty version. Most acoustic nuts cannot be switched around to do a righty-lefty conversion -- no front-to-back symmetry.
That floating bridge is good for the conversion. If the bass strings are set to a different height than the treble, you can do a 180 rotation on that bridge. If the string heights are the same low E to high e, then slide the bridge into the best position for intonation.
-=tension & release=-