What do you do in a funny animal setting about the consumption of meat and other animal products? In most cases it is just ignored or there is an unspoken understanding that the animal characters are distinct from food.
I got a few stories in before I realize this was thing. These images are from separate short comics where character are introduced to pizza for the first time. The first comic I didn't think twice about the characters eating peperoni but on the second I switched it to pineapple (I know I'm a monster). I also went as far to only refer to milk shakes as shakes to avoid explicitly stating the characters are consuming dairy.
Going forward I think I just going to show everyone as effectively being vegetarian but not explicitly depict eggs or milk. That way it could be interpreted that cheese and foods that would have eggs could have been made with in universe equivalents.