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.

Darkmoon Faire

Moon Moon

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.

Pierre

Pierre is a mechanical pet that doubles as a cooking fire

Lil Bling

Blingtron Gift Package

Rare Spawns

Ashleaf Spriteling

Ashleaf Spriteling – Drop from Leafmender

Azure Crane Chick

Azure Crane Chick – Loot from a Crane Nest

Dandelion Frolicker

Dandelion Frolicker – Neverending Spritewood

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)

Death Adder Hatchling

Drop from Imperial Python

Gu'chi Swarmling

Drop from Gu’chi the Swarmbringer

Bufo

Gulp Froglet – Drop from Bufo

Jademist Dancer - drop

Jademist Dancer – Drops from Jademist Dancers

Jadefire Spirit

Jadefire Spirit – Drop from the Spirit of Jadefire

Ominous Flame

Ominous Flame – Drop from Foreboding Flames

Skunky Alemental

Skunky Alemental – Drop from Zhu-Gon the Sour

Spineclaw Crab

Spineclaw Crab – Dro from Monstrous Spineclaw

Ruby Droplet – Drop from Garnia

To reach Garnia, use the Timeless Isle Airways

Vendor

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.

Sky Lantern

Purchased from Ku-Mo for 7500 Timeless coins

Harmonious Porcupette - Mistweaver Ku

Harmonious Porcupette – Mistweaver Ku – Requires Shaohao (Pathwalker) rep – 7500 Timeless coins

Vengeful Porcupette

Vengeful Porcupette – Bought from Speaker Gulan – 100 Bloody Coins

Siege of Orgrimmar

Droplet of Y'Shaarj - Sha of Pride

Droplet of Y’Shaarj – Sha of Pride (Flexible, Normal or Heroic)

Kovok

Kovok – Paragons of the Klaxxi

Gooey Sha-ling

Gooey Sha-ling – Sha of Pride (LFR or Flexible)

Blackfuse Bombling

Blackfuse Bombling – Siegecrafter Blackfuse

Wild Pets

World Event

Rotten Little Helper - winter veil pet

Rotten Little Helper – Feast of Winter Veil (Stolen Present)