I completely lsupport this!
I have all my pets in "Pets without a group"
Because they are all for trade, and i keep my favorite pets in a locked group. However, anytime i trade for pets that i want and the trade gets accepted, i have to go through 2300+ pets (116 pgs) in order to find the pets that i have to put in my vault, and it does get annoying often..
Plus, if you sort your pets by their species in separate groups, it would be so much easier to just click of that type of pet and then convert full pages at a time. C: