I’d recommend doing some Draenor and Pandaria trainers daily. With Warmode on, the Safari Hat, Lesser Pet Treat, and Pet Treat my Alliance alts get a carry pet to 24 with just two trainers. Probably a little less for a hatless Horde toon. Bonus for me, this also gives some nice XP for alts I’m trying to level.
I’ve mailed you on Proudmoore with some additional suggestions. Oh, and “MPD” is Mechanical Pandaren Dragonling.
Dreanor
Gargra: Your Warbot and Cogblade Raptor will work with a level 1 carry pet. Your Raptor being S/S breed it’s guaranteed, with a slower one it’s more RNG dependent.
Tarr the Terrible: My strategy uses 2 non-tradeable Hallowed End pets that you don’t have but Wowhead has other strats.
Taralune: Chrominius and Sprite Darter with a 15+ carry pet.
Vesharr: Chrominius and MPD, level 1 carry.
Ashleigh: MPD usually solos with a level 1 carry, sometimes may need a backup, preferably with strong hit ability.
I skip Cymre Brightblade cause I’m lazy and fight takes too long.
Pandaria
Hyuna: Nexus Whelpling and Fledgling Warden Owl, level 1 carry.
Thundering Pandaren: Scooter the Snail, MPD, level 1 carry.
Courageous Yon: Iron Starlette, Anubisath Idol, level >10 carry.
Burning Pandaren Spirit: My strat uses Servant of Demidos which you don’t have and sounds like a real pain to try to get. Check Wowhead (I can use a level 1 carry on this one).
Flowing Pandaren Spirit: Blackfuse Bombling (you’d need to level yours first to 20 or so level) and Ikky, level >12 carry.
Moruk: Rotten Little Helper and Nexus Whelpling. Carry pet maybe 15+, it depends on its pet type.
Farmer Nishi: I use Slithershock Elver and Dibbler to level a 12+ carry, you don’t have either so Wowhead again.
There’s several other trainers that I now skip due to laziness or because can’t reliably level any pets with them. You may want to experiment.