I'm not very into the PvP part of pet battles, so tying it to that in any way would probably mean I'd never even get it
If they ever were to add a Mini-Me sort of pet, I'd maybe imagine it tied to some gnomish/goblin teleporting mishap? (They're the number one cause of evil clones, after all.) Like, say there was a teleport you could only use once a day and every trip had a chance to spawn a miniature you that you would then have to battle and capture? I dunno!
And hey, since we're brainstorming: how would a pet like this work, being account-wide? Would it always be a mini version of whichever character you're on, or just the one you caught
it on? And if the latter, would you be able to catch one for every class in-game?