This looks like a type of wood decay fungi called Armillaria. There are several types. The fungus feeds on dead organic matter such as dead tree roots, buried logs, and stumps. These fungi may live for many years until the wood is completely destroyed.

 We do not have a mycologist on staff. There are many "look-alikes" and mushroom identification is complex (involving spore prints, etc.). We do not comment on edibility. We recommend that you contact your vet for more information. If you have concerns about the pet, you can remove and dispose of the mushrooms before allowing them in the area.

Marian