AirParrot works with the AppleTV 2 and 3. The original AppleTV does not support mirroring of any type.
AirParrot enables 1080p mirroring automatically for the AppleTV 3 on both Mac and Windows. If you notice things running slow, you can force 720p in in Preferences and you'll be all set.
Which AppleTV do I have?
The first generation Apple TV is much larger (about 7 in.²), it is silver and grey. The second and third generation Apple TV's are both black, the second-generation model has a maximum resolution of 720p (settings > audio and video > TV resolution), the third-generation model has a maximum resolution of 1080p.