This will be an issue until Mists releases - on CROSS BATTLE.NET transfers.
You have a couple options. You could contact Billing and ask this be reversed and wait for Mists to release - or wait till release, cage your pets and hand them over.
After release, you'll STILL need to cage your pets to take them with - or hand over, but caging functionality just isn't in yet.
Thanks for the reply. It's too late for me but you REALLY need to put a warning on the transfer confirmation page - what is that, 5 min labor editing HTML? This stuff is in no way intuitive, that all kinds of account-wide stuff like mounts, heirlooms, archeology epics, blizzard store items etc transfer to a new battlenet just fine, but suddenly every pet down to the Orgr cockroach are euthanized? I still don't get what caging is and if it can transfer every pet, but after MoP launches you need yet another warning on the website because I 100% guarantee no one is going to just guess they need to cage 500 pets prior to account transfer.