After a bit of research on the web based on everyone's helpful response, it would seem that our pup has tapeworm and, possibly, roundworm.
We have a vet visit scheduled for tomorrow afternoon and hope that our pup will be on the road to recovery soon.
We will be having our other puppy looked, as well, seeing that she has developed a taste for poop. Who knows what she has put in her mouth when we weren't looking.
