Q: update 10.9.1 not showing up in 'software update'

Have you tried going to the App Store and finding the update there?  Or getting the updater from the Apple Downloads site: OS X Mavericks 10.9.1 Update

OT

Open About This Mac and click on the version number once. It should show the build. What is the build number?

What happens when you try to launch and run the 10.9.1 updater?  Any messages?

My OS X Mavericks 10.9 build number is 13A603.  I also have a mid-2013 MacBook Air.  (You say "Late 2013 MacBook Air" ... what is that?  Apple did not release a MacBook Air after June 2013.)

So do you either have some experimental machine or some experimental OS X build?

The first MacBook Air was released in January, 2008.  The mid 2013 MBA came with 10.8.4 preinstalled so the Mavericks build that the OP is reporting to must have come from the App Store.

Actually, I have a mid 2013 MBA that I received about a day or two after the machine was released in June.  I got mine with 10.8.4 preinstalled (of course).  Then I got Mavericks 10.9 build 13A603 from the App Store in October.

So somehow the OP has some different configuration!  My guess is that 13A3017 postdates 10.9.1 (or is some developer build).

That must be it.  I've been on the Beta testing team but the seeds for the first go around, the A seeds are no longer listed so I can't compare them.

Where did you get the Mavericks installer from?  Did you run any other system updaters before trying 10.9.1?

Ah, OK, Mc_Lovin and Old Toad, I figured this thing out!

This article has the answer:

http://support.apple.com/kb/HT1159

It turns out that Mc_Lovin, you do not have a MacBook Air at all.  You have a MacBook Pro!  And indeed you do have a Late 2013 MacBook Pro that would not require (or accept) the 10.9.1 update.

I figured that out by looking for build 13A3017 in the article.

Good sleuthing.