Thanks to @patf0rd we now have some insight on what you earn by defeating all of the Draenor trainers.
Once you've completed the achievement Taming Draenor AND have a level 3 Menagerie (blueprints for a level 3 menagerie require the achievement Draenic Pet Battler), you'll unlock a new daily quest inside your garrison called "Mastering the Menagerie" (NYI on Wowhead). The objective of the daily is to defeat all 6 trainers.
It will reward a Big Bag of Pet Supplies which contains charms and the family-specific leveling stones. Plus, it might drop some new pets! Well, at least according to the Pet Journal. There are a handful of pets that are rewarded from the quest "Mastering the Menagerie".
A big thank you to patf0rd for sharing this info with me and testing all of this out!
Edit: List of all the pets that are currently listed in the beta Pet Journal as a reward from "Mastering the Menagerie". There's a total of 7.