Well if you want the food system to be similar to the clickpet system, its totally doable. You may want to create a table called food to store all available food and a few columns in table prefix.adoptables to specify each pet's favorite and least favorite food.

Wondering if this feature could be considered in a plug-in/mod instead of in the main game. Or make sure it is something that can be turned on or off. I don't like messing with food, hunger, happiness in other pet games and will not play them if it becomes an insane process to upkeep pets, and I don't want them in my game.

Well in Mys v1.4.0 everything can be turned on and off, even the registration and click-pet system. It is good for admins to experiment certain features on their sites without having to worry about users actions mess things up. In Mys v1.3.3 though, only the breeding, pound and trade system can be turned on/off.