The count is zero and the array is empty for a character such as mine who hasn't logged in since MoP launched. I know things have changed and pets are now "Battle Pets", but maybe this was an oversight?
I can't tell if it's for characters who haven't learned how to battle, or if it's just not logging in. It may apply to new characters as well, but I can't test it.
http://us.battle.net/api/wow/character/stormreaver/Rinn?fields=mounts,pets