Binny the cat heads to the neighborhood park to meet the members of Friendly Pets, Chapter 9. As Binny gets closer to the park, she sees a thing glowing under a nearby oak tree. Binny studies it and twitches her whiskers to catch a scent. It looks like a glowing ball, but noisy.

Binny realizes whatever it is, it's just a baby. She decides to adopt it and hides it in Mrs. Cobbler's basement. Because she found it under a full moon, she names it Moon Girl. She feeds and cares for her flashing and whizzing Moon Girl. Ariel, Mrs. Cobbler's niece, comes for a visit and discovers Moon Girl and promises to keep her a secret.

One day Binny notices Moon Girl isn't glowing as bright and her round body is getting flat. She enlists Ariel and the Friendly Pets club to help save Moon Girl's life. Binny and Ariel decide to take Moon Girl to the local vet. Much to Binny's alarm, the vet keeps Moon Girl for scientific study.

In a race against time, Binny and her friends have to save Moon Girl from the vet and find a safe place for her to live in peace.