Actually, I do have a vague idea for the skill particulars, but there are some things you'll have to figure out or ask others. Wolpak and Kva3imoda are a few that might know about the things I'm unclear on.

Give those big pets an active skill with the following characteristics:

1. Set the cooldown to the rate they should eat fish.
2. Leave the animation field BLANK. No animation.
3. Activation type should be ANY.
4. Target type = self.

5. On EVENT_START fire a damage shape to check for enemies. Set it so it only checks for enemies at the layout level.
6. On EVENT_UNIT_HIT, add a stat called something like IN_COMBAT to the pet.
7. Set another EVENT_START above the EVENT_UNIT_HIT (? I can't remember the order of operations right now, put it to fire after the UNIT_HIT, you can find the answer in Wolpak and OedipusTex's conversation about making toggleable abilities on the Runic forums). Give this 2nd EVENT_START a STATWATCHER that requires the pet to have a IN_COMBAT stat of 0. This Event should fire the layout that initiates the subtraction of the fish and any accompanying graphical indicator that your pet is a glutton. This is the part I don't know how to do.