There's a way around this problem, which is actually quite obvious once you think of it, yet roleplayers rarely use it, so far as I have seen. If you write the possessive apostrophe-S as the first part of your character's custom emote, you can make your pet seem to do something on its own: "Isabeau 's pet wolf growls and bares his teeth." It takes a little bit more typing, and it leaves a space between your characters name and the apostrophe-S (since that's built into the emote system), but effectively it lets you roleplay two entities at the same time. Hunters and warlocks can use the PetEmote addon to help make this a little more streamlined.
Our reader Ellyndia, for instance, roleplayed a very introverted character that normally would not introduce herself to others, but using such custom emotes, she could have her Jubling walk up and interact with people first to get conversations going. Pets can reflect what your character is thinking but not saying out loud (by hissing or purring perhaps), or they can do anything that such pets in real life might do. Special non-combat pets such as the Children's Week kids, the interactive Animatronics, or even the magical Mojo, could all be especially fun to animate a little now and then. Certainly this technique would become very annoying if overused, but in moderation it can add a extra spice of humor, entertainment and even a touch of realism into the game.