Getting Apple TV 2 to work with third-party iPad app
From Apple's Apple TV 2 AirPlay page (in the footnotes at the bottom of that page):


  
  AirPlay is available on all devices running iOS 4.3 or later. Some features require the latest software. Second-generation Apple TV or later required.
  AirPlay Mirroring is available with iPad 2 or later; iPhone 4S; iMac (Mid 2011 or newer), Mac mini (Mid 2011 or newer), MacBook Air (Mid 2011 or newer), and MacBook Pro (Early 2011 or newer) with Mountain Lion.
  


This explains your situation as far as what you're describing, which sounds like mirroring. In my experience with the 1st gen iPad, there is usually a speaker icon next to the name of your Apple TV when you are attempting AirPlay and audio-only capability is available. When you're using hardware with video AirPlay capability (i.e., Mirroring), there is a TV icon next to the name of the Apple TV. Beyond the footnotes listed above, this is a sure indicator of your iPad to Apple TV connectivity options.