Leveling a new pet from 1 to 25 can be a time-consuming slog -- but it doesn't have to be. Though you'll need to start with a few solid level 25 pets, you can let two max-level pets carry you while saving your third slot with a that needs the experience. Then, just fight your way through high-level pet trainers with this guide from Adventures in Poor Taste. The trick is in having the right level 25 pets so you can win battles without having to rely on your third, under-level pet.
The guide walks you through the ideal pets for the job -- you might want to hit up their guide to the 7 best beginner pets while you're at it -- and gives you a play-by-play for what to expect from all of Pandaria's pet trainers (plus a couple of extras). So what are you waiting for? Break out your Safari Hat level your way up to the 30 max-level pets you'll need to enter the Celestial Tournament. Good luck!