Just look at this massive list of Timeless Isle pets. Not surprisingly, a lot of them come from the rare spawns on the Timeless Isle, as well as other sources.
Celestial Tournament
To collect the Celestial pets, you will need to complete the Celestial Tournament ten times.

Chi-Chi, Hatchling of Chi-Ji (Flying)

Yu’la, Broodling of Yu’lon (Dragonkin)

Xu-Fu, Cub of Xuen (Beast)

Zao, Calfling of Niuzao (Beast)
Darkmoon Faire
Moon Moon drops from the new Darkmoon Faire boss – Moonfang
Unique Abilities: Moon Fang, Moon Tears, Moon Dance.
Profession
There are three engineering pets: two are made while one is obtained from Blingtron.

Rascal-Bot is a tribute to the Bad Robot Productions mascot

Pierre is a mechanical pet that doubles as a cooking fire

Blingtron Gift Package
Rare Spawns

Ashleaf Spriteling – Drop from Leafmender

Azure Crane Chick – Loot from a Crane Nest
Interact with the Neverending Spritewood (purple rare spawn crystal) and kill Scary Sprites (note these are the larger sprites which can randomly spawn as opposed to the smaller Angry Sprites) – (45.4, 73.3)

Jademist Dancer – Drops from Jademist Dancers

Jadefire Spirit – Drop from the Spirit of Jadefire

Ominous Flame – Drop from Foreboding Flames

Skunky Alemental – Drop from Zhu-Gon the Sour

Spineclaw Crab – Dro from Monstrous Spineclaw
Ruby Droplet – Drop from Garnia
To reach Garnia, use the Timeless Isle Airways
Vendor

Bonkers – Kukuru’s Cache Key
Collect Bonkers by opening Timeless Chests inside Kukuru’s cave (59, 40) on the Timeless Isle. You will need to purchase a Kukuru’s Cache Key for each chest you wish to open. Each one has a small chance of containing the pet.
Purchased from Ku-Mo for 7500 Timeless coins

Vengeful Porcupette – Bought from Speaker Gulan – 100 Bloody Coins
Siege of Orgrimmar

Blackfuse Bombling – Siegecrafter Blackfuse
Wild Pets
World Event

Rotten Little Helper – Feast of Winter Veil (Stolen Present)
Skunk beer…lol!!!
Considering how the rare is summoned, it makes perfect sense! :)
Oh boy, I’d better get busy leveling what I already have, so much more incoming!
That’s for sure!
I’m looking forward to getting Zao and Xu-Fu =)
Xu is my fav :)
I can’t wait to grab some of these, especially the Spriteling and the Rascal Bot. So glad they just keep adding them.
I am too. 1k collections doesn’t seem that far off at the rate they’re going.
Rascal-Bot and Pierre!!!!
I can’t wait. Times like this i’m glad I’m an engineer :)
My thought exactly!
Ashleaf Spriteling, so this is from Leafmender only not from also killing sprites? Gu’chi, same question, not from killing the smaller caterpillars? I thought these could be farmed from the mobs as well as drop from the rares.
According to the Pet Journal they only drop from the rares.