"Page isn't working"!
No reason why you shouldn't have airships. Do you also have aeroplanes?
Yes, I'm thinking there will be aeroplanes. Biplanes probably. Don't think they'll be steam, though. Maybe powered by imagination... or internal combustion.
I really can't tell from the OP why his world is the way it is. Is there a good reason in the alternate history why steam cars would be common instead of light and powerful internal combustion?
There's a good reason yes. It's not the main reason, but it's not alternate history, it's another world/planet/existence/[insert plain of existence here]. I can't give too much away now.
Thanks, all. See, you're all hooked now, right? Now the trick will be to try and write "American" and not flip back to my natural, dry British tastes and mannerisms.