I took Pip to a nearby animal clinic to be checked for a microchip and to see if they could determine the kitten's approximate age and gender. The clinic was closed for the holiday weekend but fortunately there were some ladies working inside. One of them had been out walking a dog and saw me at the door. When I told them why I was there, they let me in.
It ends up that Pip is about 6 weeks old and is a girl! She has a little ringworm on one ear but other than that, she's in good health. They have a kitten care plan at the clinic so I'll bring Pip back there when I'm ready to start her on that. I'll probably switch Squirt over to this clinic, too, since our old vet's office is so far away from where I live now.