Is it possible to get digital audio output from a MacBook Air (2011), like on other Macs?

Yes its possible and here is an example of a USB to Digital audio output adapter, just like the ones found on other Macs, but external.

Turtle Beach Audio Advantage Micro II USB Analog & Digital Audio Adapter

I had the same problem. I got some cheap thing off the ebay that will split out analog and digital optical from the hdmi. It makes one less cable to plug in to 'dock' the air to the tv.

You can use a USB A-B cable to connect from the usb port to an external DAC if the DAC supports USB, which many do. I recommend Schiit's products, mine worked without a hitch from my macbook air.