Blizzard announced that a new feature will be introduced in the upcoming patch 4.1, Dungeon Finder: Call to Arms.
In a Nutshell
This system is intended to help shorten level 85 heroic five-man queue times by rewarding players who take on roles that are least represented in the random dungeon finder. If eligible for the additional rewards, players will receive a goodie bag containing gold, gems, and possibly a vanity pet or even a rare mount.
"The pets offered come from a wide variety of sources, and include companions like the Razzashi Hatchling, Cockatiel, and Tiny Sporebat"
Only three pets have been announced as potential drops from the reward bag so far, but there are likely to be other companions in the loot table.
How to Qualify
To be eligible for the extra rewards and a chance at a vanity item, players will need to solo-queue as the role that is currently Called to Arms for a random level 85 five-man heroic dungeon, and kill the final boss of the instance. The random dungeon finder will announce which role (tanking, healing or DPS) qualifies for the goodie bag.
There is currently no cap or limit to how many times a player can qualify for the additional rewards each day. This potentially means another method of grinding or farming for a desired pet (albeit quite random) while working towards gearing up and experiencing five-mans at the same time!