But the UI is there, anyway.
You open the stable from a Stable Master NPC like always. There are 5 slots -- the active pets -- down the left-hand side of the UI and 10 slots under the picture of the currently selected pet. There are two pages on the bottom, for a total of 20 inactive slots.
Right now you can drag the pets anywhere within any of the slots. Hopefully that stays that way -- it would be handy for organizing your inactive pets.
Unfortunately there doesn't seem to be any way to use Call Pet to get at any but the first active pet right now.
Oh ... and note that these pictures were taken by a level 10 hunter. At the moment, at least, there does not seem to be a cost for the expanded stable.
(My thanks to Maia for struggling with login long enough to take these screenshots!)