I was sorta looking for that as well, but then i realized that you can search on ability name.
Although it is not actually sorting pets, but that would be pretty difficult anyway.
How would you order them, choosing Meteor Strike will only put 4 pets in a group, and choosing Magic abilities is not going to narrow things down much either, because some pets have multiple family abilities.
Best thing would be to just search for the specific abilities, on here or in the WoW pet collection itself.
One thing is annoying though, some abilities are the same as other ones, the only difference being is the name and family it associates with. Which can lead to pets being overlooked because i dont know the other name of the similar ability.
Like Bleat vs Haunted Song, or Swarm/Stampede vs Flock etc.
(maybe a tip for the site to put up a "similar ability to" for comparison? If it is already there, then ignore this
What also is annoying is that some abilities share icons with other abilities, like Consume Corpse vs Creepy Chomp, sometimes i picked a pet because i thought it had Consume, but in battle it turned out the be a Chomp, that is my fault of course, but it can be confusing when you're sifting through pets, luckily that only happened twice, with the same pet as well (Creepy Crate).