The good news was that it is now available for Android and my wife successfully installed it on her S4. When I went to install it on my S4 Active, I got the "this device is not supported." I also struck out installing it into our Asus Transformer TF300.
So I downloaded an .apk backup app off of the Play store, extracted DisneyJunior.apk. Moved it to both my S4A and our TF300 and it installed and plays fine.
I would suspect that the Watch Disney Junior app works on a LOT more phones/tablets than is officially supported.