I think that I would fill that back in. If you don't, it will likely erode as rain gets in there and grow larger. I would also figure out a way to keep the dog from digging. Red pepper flakes mixed into the dirt worked for my dog.
People get the idea that the pressures exerted by an AGP are insane because the total weight is insane but it's spread out, imagine the pressure at the bottom of a 4ft high stack of full soda cans that's roughly equivelant.