Commenters have raised the issue of lagging out due to a pet’s having eaten the router. They went on to start the real question: how much will this affect performance, and how can we mitigate it?
Is your dog small or thin enough that a wireless signal can still get through? Will it matter if you have a long-haired cat? Are the essential pieces small enough that they could be sufficiently whole after the plastic case has been devoured? And how much battery life does that thing have?