Under filters, you can EXCLUDE duplicates, but there's a much faster way to do it. I just analyzed your collection, so these details are unique to you, but can be adapted to any collection.
Go to your collection on WCP, and sort by rarity. Go to the last page. You'll see the four non-combat pets you have that will always show as uncommon, even if you've used a stone.
Then go back each page until the greyed out duplicates STOP. For you this is page 7.
You see you have two other uncommon pets that are "firsts" in your collection. The Royal Moth and the Snowy Owl. Thus, there are your six pets.
Thaliana#1794 - My WoW account has 50 toons, so I would so greatly appreciate people creating toons on Kael'Thas or Ghostlands to trade with me. <3