I think it would be cool if you could adopt an orphan from the orphanage in Marleybone...either a pup boy or kitten girl (or both, I guess). They'd act like (and take the same slot as) pets, but instead of attacking, the pup would run up to either you or one of your companions and 'cheer' the target on, granting a small, 1 round bonus to attack, and the kitten would do the same, but heal a small amount of damage instead. When either is defeated they burst into tears and run off the field. Since they technically aren't 'pets', they wouldn't be available for hatching or pet combat, but they would gain experience based on your level, and maybe even get bigger as they advance (they're 'growing up'!)
Some other ideas...
I just started a new pirate, and noticed how neat the lava fish look in the waponi volcano, now that they're on fire! I'd love to have a flaming fish pet!
I've always wanted a juju chicken pet...he could have the Witch Hunter ability, and he'd explode into a cloud of feathers when he is defeated.
Also, pet versions of the following monsters; storm shark, hornet, (cherryblossom) treant, jellyfish*, manticore, and colossus
*(the really glowy ones like in the Cave of the Crescent Moon)