I don't have precise numbers, but I tend to level with the daily quests.
I have alts parked at Jaguero Isle, Skulk Rock, and Karazhan for some of the rarer battle pet spawns, which are very close to tamer dailies: Bill Buckler (lvl 11), David Kosse (lvl 15?), and Lydia Accoste (lvl 21). I do these in sequence, it gets a level 1 roughly to 5, 8, then 10. 10 is high enough to survive a hit from a Pandaria tamer pet, so I then do the 7 Pandaria dailies, which is enough to get up to 22 or so. There's several other rare pet spawns that are very close to tamer dailies: Shadowmoon Valley, Searing Gorge, Onyxia's Lair, Argent Tournament, Felwood, Sporeggar, Shattrath/Razorthorn Ridge, possibly others depending on what you're hunting for.
My daily quest team is the lowbie, Darkmoon Zeppelin, and a third pet that can mostly solo each particular tamer. I mostly use Magical Crawdad, with Spawn of Onyxia for the Dread Wastes tamer and Emerald Whelpling for KunLai, Jade Forest and Krasarang. I let the Crawdad/Emerald die late in the fight, then the main purpose of the Zeppelin is to get the last killing blow with Explode so that the lowbie pet gets the entirety of the XP reward, which is roughly 2k per Pandaria daily.
My guess is this takes ~40 minutes of total time, due mostly to the travel in Pandaria. Therefore Doobjanka's method is likely more efficient if you only care about pet leveling, but I'm doing the dailies for the bags anyway, so it's only a little bit of extra effort.
Also, I really want a Netherwhelp...