Yes, Pet Food is only available through the Item Mall or purchasing off other players (can be expensive).
However, Pet durability is pointless. The purpose of the durability is so that your pet will help attack if you set them into Attack mode. They will still loot items even if it's 1/100.
Personally, I don't care about the pet attack. It's pretty weak and if you set it into Attack mode, it has a harder time to loot items if you don't stop to give it time to pick up the items. A continuous attack on monsters around you just means more items lying on the ground and your pet chasing after the targeted monster.