Here are the top 20 priced pets that can be farmed from drops:
1. Spineclaw Crab, drops from Monstrous Spineclaw, Timeless Isle.
2. Rebuilt Mechanical Spider, part of Voldun invasions, Zandalar.
3. Rebuilt Gorilla Bot, part of Voldun invasions, Zandalar.
4. Coldlight Surfrunner, Island Expeditions, Zandalar.
5. Moon moon, drops from Moonfang, Darkmoon Faire.
6. Filthy Slime, drops from Gol'than, Tol Dagor mythic, Kul Tiras.
7. Knock-off Blingtron, Blingtron 6000 gift package, Engineering.
8. Spawn of Merektha, drops from Merektha, Temple of Sethraliss, Zuldazar.
9. Baby Stonehide, Island Expeditions
10. Tonguelasher, Island Expeditions.
11. Living Fluid, drop from Primordius, Throne of Thunder, Pandaria.
12. Rotting Ghoul, Island Expeditions.
13. Jadefire Spirit, drop from Spirit of Jadefire, Timeless Isle, Pandaria.
14. Sprite Darter Hatchling, world drop, Feralas. Best drop rate is from Sprite Darters.
15. Shadefeather Hatchling, Island Expeditions.
16. Black Tabby Cat, world drop, Hillsbrad Foothills. Best drop rate from Syndicate Spies.
17. Firefly, drop from Bogflare Needler, Zangarmarsh, Outlands.
18. Fox kit, drop from Baradin Fox, Tol Barad, Cataclysm PvP zone. A pet may also drop from Elementium mining nodes here.
19. Azure welpling, world drop, Winterspring, Wrath pvp zone.
20. Voru'kar leecher, Island Expeditions.
Let's break these into categories.
The first farm is Island Expeditions. Patch 8.1 introduced new expedition pets and a revamped loot system that makes all pets easier to get. However it's clear that demand is currently above the level of supply. Over time that will change as people run expeditions and find pets quite accidentally, with many of them going to the Auction House. It's still possibly the best pet farm in the game at the moment and has the side attractions of gaining your character Artifact Power and Seafarers' Doubloons. 100 Doubloons gets you a Crimson Octopode pet currently worth 77k. (there's also an albatross pet but that has a lower gold/dubloon rate).
It's best in my opinion to do this at the start of the week as even those few days allow prices to drop significantly. However there will probably be another surge in the prices when the 8.1 raid lands in late January and people come back to the game to do the raid (and buy pets!)
Next is the Voldun invasion that only seems to pop in the small hours of the morning. Very worthwhile doing if you happen to be up.
Next are Pandaria farms mostly based on the Timeless Isle. There's also a weekly pet tournament there which gives non-tradeable but very strong pets.
Darkmoon Faire starts on 6th January and offers a ton of pets. It seems better though to spend your tickets on transmog, sell the transmog then use the gold to buy things like Darkmoon Tonk if you want them.
There's a couple of nice ones from Mythic + BFA dungeons. If your group doesn't mind where they go then the chance of getting a 50K pet might be worth considering.
The Blingtron pet is super rare. It's possibly not worth levelling Engineering for but if you see a blue ! on your minimap while in town it's well worth a click.
The drops in low level Vanilla and TBC zones make farming those mobs a possible way to level an alt. Just burn through all your rest exp killing Sprite Darters to occasionally get a sweet gold injection.
I assume the pvp zones that give the pets are pretty much dead now. Could be another good alt leveling spot.