Diagnosing 2011 Macbook Air Webcam
Chances are your OS X installation is broken.

First run Apple Hardware Test, restart and hold D.

Still not showing in System Hardware profile ? Slim chance but it wont hurt, reset your SMC and PRAM.

Still not working ...

Make backup to Time machine (external drive)

Restore your OSX , restart and hold Command-R that will get you in to Restore screen. Follow the instructions.

Still not working...add new MacBook Air to your Christmas wish list.

Buy a cheep USB video camera so you can survive till then.