Anubisath Idol, Clockwork Rocket Bot, Clock 'Em, Corehound Pup, Darkmoon Tonk, Iron Starlette, Pandaren Monk, Nether Faerie Dragon, Spirit of Competition, and the Zandalari raptors are all clutch pets that are needed a few times over for some of the more annoying pet battles, especially the Celestial Tournament.
Also if you don't have a Pandaren Water Spirit, Chrominius, Unborn Val'kyr and Nordrassil Wisp, you'll need to acquire those because they are also relatively important.
I'm sure there are a few more I missed but the ones I listed tend to be the most important.