Everyone from Apple and other retailers that I talked to about the mirroring accessory assured me that it worked with iPad1.
It turns out it doesn't.
Careful reading of the package label says that the mirroring is only available with iPad2. It will work with other devices to show video and photos.
We are lucky enough to have been able to purchase an iPad2 and one of the first things I did was plug in the digital AV adapter.
It works like a charm!
Now I just have to figure out how to connect it to non HDMI equipment!