I have a MacBook Air (13-inch, Mid 2011) with 1.7GHz dual-core Intel Core i5 with 3MB shared L3 cache processor, and Airplay MIRRORING menu still does not show up in the menu bar. I have just updated my software (10.7.5). I can use Airplay with iTunes but no mirroring menu shows up in the dock as specified in the how to. System Preferences > Display does not show any option to show Airplay mirroring in the dock.
You need OS X Mountain Lion (10.8) to use AirPlay Mirroring