I would definitely look at the old 5.3 pet trainer guide to panda tamers it has a limited number of pets that can be used to carry pet the tamers and get your other teams up to 25 in a hurry. I know even without pet treats I can level 2 pets from 1 to 25 in an hour on autopilot mostly.
Here is the limited rotation you will need to follow the
5.3 guide while leveling pets for the
5.4 guide which will get you into Draenor quickly:
Pet Shop
Below, you will find the list of all the pets required to complete all the teams you will find in this guide:
5 battles
Darkmoon Tonk [-]
4 battles
Chrominius [-]
Emerald Proto-Whelp [4] (Uncommon rarity acceptable)
Snarly [-] (other crocilisks acceptable)
2 battles
Anubisath Idol [-]
Grasslands Cottontail [5]
Mechanical Pandaren Dragonling [-]
Pandaren Water Spirit [-]
Vampiric Batling [-] or Bat [4]
Yellow Moth [4] (Uncommon rarity acceptable)
1 battle
Sunreaver Micro-Sentry [-]
Darkmoon Zeppelin [-]
Emperor Crab [4]
Eternal Strider [8]
Flayer Youngling [5] (Uncommon rarity acceptable)
Infinite Whelpling [4]
Scourged Whelpling [6] (Uncommon rarity acceptable)
Spirit Crab [6] (Uncommon rarity acceptable)
Unborn Val'kyr [?] (any breed acceptable)
Zandalari Kneebiter [4] or Zandalari Anklerender [14]