I'll pick up a stone and upgrade a non-battle pet other than the Darkmoon Balloon.
I also am seeing a problem with the Dragon Kite though. The Armory lists it as Epic and my pet journal has it as rare, however Warcraftpets.com shows the Dragon Kite as Common.
(Others have mentioned this already, but wanted to confirm that I'm also seeing that.)
I'll update tonight after I test a battle-stone on a non-battle pet.