There have been quite a few pets that match different races, classes, and even specs. I know my Pandaren Shadow Priest always has a Gooey Sha-ling or Droplet of Y'Shaarj following her (going with her Glyph of the Sha and LFR Horned Nightmare recolor quite nicely). Druids have plenty of critters and plants to follow them. Monks have babies of the August Celestials that are quite perfect for them, or even a Pandaren Monk. Warlocks even have a few demons (to go with their demon pets).
However, there are very few "holy" pets out there. The only ones that come to mind are Mini Tyrael, Murkalot, and the Unborn Val'kyr - which the last one could be considered better for a Death Knight than a priest or paladin. Non-battle pets include the Argent Squire and Argent Gruntling. A semi-holy pet would be the Nordrassil Wisp and perhaps the Spirit of Summer for Night Elf priests or druids.
Thinking of other pets that would be suitable for our paladins and priests was, actually, difficult and fun. Here's what I've come up with.
Guardian of Ancient Kings, it would be a perfect little pet for paladins. It could be a wild pet (the first I've suggested, I believe!) from Arathi Highlands - specifically Stromgarde. I can't think of more of a place with more "ancient kings" than the first human empire.
The model for the pet could be the actual model itself, but I would prefer a Mini Tyrael/Unborn Val'kyr model made to look like the Guardian. That would be fitting, as well as adorable. This pet could be a humanoid or magic pet.
For abilities, it could have any combination of moves from Murkalot and Mini Tyrael, up to and including: Righteous Inspiration, Restoration, Holy Charge, Holy Justice, Holy Sword (or, a renamed version, considering Tyrael's sword name is in the description), Omnislash, Surge of Light, or any other light-based moves. Fortunately, Murkalot and Mini Tyrael have the most suiting moves for this little guy.
The Redeeming Spirit could be another wild pet, found in graveyards around the world, particularly in starting zones, such as Elwynn, Durotar, Dun Morogh, Mulgore, etc. It would be an easy pet to find (realm permitting, of course) and would be fitting in graveyards where their larger sisters hang out.
For abilities, it could have Spectral Strike, Ethereal, Call Darkness, Light, Restoration, and Unholy Ascension. That set of moves would all work together fairly well, and she would definitely be a pet people would want to use in some tougher battles.
The next post will have Naaru pets. Let me know what you think on Twitter!