Well, granted, the title is a bit misleading since there technically isn’t any pet food store. Most Hunter pets eat items you can catch on a hook, carve off an animal, or the fruit vendors. But, as of Patch 4.1 it really won’t matter.
If you’ve played a Hunter, this picture isn’t a revelation. Your pet is happy, it does more damage. Aside from a talent point that allows your pet’s happiness to increase the more it’s in battle, the only way to really keep your pet happy is to feed it. Again, in Patch 4.1 that’s going to change.
The developers are removing the feed your pet buff/keep your pet happy buff. Tamed pets will simply be happy just be in your aura of awesome. The only bonus to feeding a pet is that it will automatically restore 50% of the pet’s health. Of course, you can only do this outside of combat.
Personally, I think it’s another little thing that’s making the game more “going through the motions” at times, much like Rogues used to make their own poisons. Did players really complain about this mechanic? Personally, I thought it was kind of amusing when a pet just left. It got annoyed or hungry enough that it said “screw you” to its master. It was a small responsibility, at best, that just added that little something to the class.