I have OSX Lion installed and upgraded to Mountain Lion to enable airplay mirroring. My Mac Book Pro is late 2011 so it should work. I cannot see the airplay mirroring menu extra in the menu bar and also it is not in system preferences > displays.

So are you saying you do not see this display at the bottom of System Preferences > Display (which comes directly from the article you attached)?

Assuming your Apple TV and Mac are on the same network, these suggestions come from the HT5404 article you attached:

___

Your Apple TV may be asleep. Simply press a button on your Apple TV remote to wake it up. After a few seconds, the AirPlay Mirroring menu extra will appear.

Make sure your Apple TV has the current software update installed.

___

Firewall security settings

If you use the firewall, make sure the following firewall security options have been set to allow AirPlay Mirroring to work:

1. Choose Apple menu () > System Preferences.
2. Click Security & Privacy, and then click Firewall.
3. Click the lock icon to unlock it if it's locked, then type an administrator name and password.
4. Click Firewall Options.
5. Uncheck (deselect) “Block all incoming connections” checkbox.
6. Select (check) the “Automatically allow signed software to receive incoming connections” checkbox.

It sounds like your WiFi network is either not too speedy or includes obstacles (e.g., firewall) that slow it down.