As good as pets are now that you can train them, why not make them even more enjoyable? For example: instead of changing from egg, to their normal form, why not make them small at first, and slowly grow as reach teen, adult, and epic (like plants) and make them glow or some other special effect at ancient!
Another cool thing for pets would be pet clothing! The problem with this would be finding cloths that fit all pets. Maybe a hat, or clothing that changes depending on the pet (or pet school type). The cloths can improve energy, or how much xp the pet recieves, or maybe it would help in the pet derby!