I bought a bunch of the shop pets on sale, and they all went to the inbox of my main toon (last logged in). Except one. One of the two Moonkins went to the mailbox of an alt on an off server I haven't logged in on in about 6 months. Just in case anyone else has issues with shop pets not showing up in your mail.
What he said. While you will see both moonkins in the journal, you can only summon or battle with the one for your current toon's faction. So you'll have to dust off your unplayed alt if you want to get them both leveled up.