The Solipsistic dog philosophy is thus; one can truly only know that one’s self exists and that anything outside the mind, such as the external word, can not be known to exist.
Pre-Socratic Greek philosopher Gorgias first theorized this philosophy and it was further developed by Plato and Descartes.
Nothing exists; Even if something exists, nothing can be known about it; Even if something could be known about it, knowledge about it can’t be communicated to others.
– Gorgias (485-375 BC)
Your Solipsistic dog will not care what the other "good dogs" are doing. They will have no concept of what other dogs do, as only their own circle of reality is all they acknowledge.
The Solipsistic dog sits firmly convinced there can be no other way of looking at life. They are not only DOG, they are all this is DOG and there can be no other.
Therefore, your Solipsistic dog believes that the whole of reality and the external world and other people are merely representations of the individual self, having no independent existence of their own, and might in fact not even exist.
So why the heck should your dog bother to go outside to poop? The mental gymnastics required by a canine belief in the Solipsistic philosophy would leave no energy for something as mundane as going to the bathroom outside.