It was quite unexpected that the "elite pets" quest would reward an achievement that unlocks a daily quest of the same nature. Defeat elite pets each day? Does that mean they'll be commonly found?
Trin on Twitter found the answer on the PTR. Elite battle pets seem to be named that are specially marked with a yellow paw print instead of the standard green one.
This will make it loads easier to complete the daily each day, and obtain the Fabled Pandaren Pet Supplies reward. Many speculate that the other panda pets (other than the red one) will be random drops from the bag. It's entirely possible since their source is listed as a quest reward, much like the pandaren spirit pets.
If this is true, we'll likely be doing the elite battle pets daily for a while since there are 3 different panda companions to collect!