The Google app does include Google Goggles, but you won't find it under the Apps button at the bottom. Instead, on the search screen there is camera icon. You tap that to go to camera mode, where you can take a picture and see the colorful squares scan your picture.
The Google app is universal and works fine on the iPad 2; however the camera is not as good, so don't expect the results to be as reliable. Though in my three tests (2 DVD covers and a jar of JIF peanut butter) both devices worked fine. I did have to log in with my Google account on the iPad before it would give me results. There was a button provided at the bottom of the camera page warning me, and providing a quick way to log in.
In my experience most of the UPC and other scanning software works fine on the iPad 2, though if it is not universal you have to put up withe small or 2x pixel view. The camera typically requires a bit more care to position and focus. It is more sensitive to bad light, and of course more awkward to position correctly.