A few checks to make; Press 'P' and check you've got batte pets trained, if not, go see the trainer in Stormwind or Orgrimmar (guards will point the way).
If you've done this, check your pet tab. There's no hotkey, but it's the image of a horse on your quicklinks bar. It also has a mounts page, so make sure you're in the pets tab. Is there a pet shown in the top of the three slots? If not, drag one from the list on the left.
One final check - does the icon for the pet have a big red X across it? If so, that pets dead and needs healing, click the bandaged cat icon on the top right of the pet screen.
If it's none of the above, it may just be a bug (I also experienced a similar bug at one point). Logging off and back on should do it, if not, you'll need to make a support ticket