Different levels/quality of pets

[Jorit]

So should you try and get different levels/quality of pets.

So should you get a common/uncommon and rare rabbit for example?

[Hydramith]

There's no good reason to keep a lower quality of a certain pet if you already have a rare, unless it has better stats and you plan to use an upgrade stone on it.

So I guess the short answer is no, you shouldn't keep different qualities. Different levels, well, maybe if you plan to use them for PvP purposes or so at different levels.