AirPlay not working!
My only option in AirPlay is iphone, it's not giving me the option of mirroring or Apple TV
iPad, iOS 5.1
Do any other devices see the Apple TV? Is your iPad really running iOS 5.1?
Take a look at this article. Note that you may need to go to another article within this one to find your answer.
Use AirPlay to wirelessly stream content from your iPhone, iPad, or iPod touch - Apple Support
Get help using AirPlay and AirPlay Mirroring on your iPhone, iPad, or iPod touch - Apple Support
You may need to update the software on the Apple TV
How to update software on your Apple TV (2nd and 3rd generation) - Apple Support
Also this person had a similar issue that was resolved.