Pet collecting is generally a personal affair. You collect pets for your own pleasure and amusement. Unlike other gameplay, grouping to hunt for pets doesn't really work out since you can't really share the same exact companion.
But where there's a will, there's a way!
You might not be able to "raid" pet collecting, but you can definitely help out fellow collectors, friends, and guildmates. No, you can't capture wild pets for others since those companions aren't cageable. However, there is something you can do with one or two other players who have the same goal in mind as you: collect all the things!
If you're in the same area as friend, and you happen upon a rare quality pet that you already own, you can alert the other player to head over to your position. Once they're there, press "alt F4" and that will forcibly quit the game.
When you do this, it will kick you out of the battle without despawning the pet. Then your friend can take over and battle/capture the rare that you stumbled on!
Everyone wins in this situation. You suffer no losses since you already own the rare quality pet, and your friend gets one too. Hopefully they will reciprocate the favor someday. :)
Using the "alt F4" method to remove yourself from a battle without despawning the companion doesn't have to be just for guildmates and friends, though. If you feel so inclined, you could also use it for all pet collectors. Should you come across a rare that you already own, rather than killing it in battle, you could let another collector have a shot at it.
It would definitely be a considerate and generous but not mandatory thing to do, since it does take time and effort out of your gameplay, but think about how happy another collector will be when they find that rare pet you've left behind. :)
So whether you reserve this for just friends, or want to use it to help out everyone, or not at all, spread the pet love! :D