Webb seems to understand the implication of having dogs in heaven when he writes, “Theologians will have to explain how petting a dog in the presence of the divine could be as fulfilling as contemplating eternal, silent truths.” But this doesn’t need much of an explanation.
Consider what God is—His quiddity, so to speak. God is omniscient, omnipotent, omnipresent, and all-perfect, just, and merciful. God is all those things, and He also just is—God is existence itself. Being in the immediate presence of such a being would be more fulfilling than anything on earth. As good as dogs are, why would they be needed in such an environment?
Perhaps this view is pessimistic by human standards. Dogs may not be necessary, but they can still be provided. Maybe. But I wouldn’t bet on it.