IIRC, the 11" MBA has a screen resolution of 1366x768. You will not be able to make the screen do higher than the max resolution (there are not enough pixels), but it can do resolutions lower than the max.
It still of course is at 1366x768, but if you use Airplay to ATV you have the option to scale the screen to interpolate a desktop space of 1920 x 1080.
I've done this a couple of times at home, and my eyes are good enough that I could handle this resolution on a screen of this size for decent periods of time, but the fuzziness is a bit much. But as a web dev it does has some utility, esp. when I'm proofing mocks vs. live changes for brief periods of time. It also makes me anxious for a rMBA. Sometimes I use Air Utility to hook up to my iPad but that's pretty slow.
So I think the question here is there a hack of some sort, some way to make a MBA believe it is connecting to a 1080p Airplay device?