The book, a primer in The Child's Own Way Series, is illustrated by Lucille Enders2 and Matilda Breuer.3
The plot of the book is not very involved, of course. A brown dog named Wag finds an owner. And a white cat named Puff finds an owner. Together, the children and animals have some adventures and learn some things. Much of the narrative, as it is, is centered around an extended visit to a farm.
At the end, Billy says, "Oh, Father, how I wish I could live here always! I like it here. When I am a man, I am going to be a farmer."
Here is a series of neat pages from the book, the first few of which describe how Wag and Puff meet their new owners.
1. Even the endpapers of the book have a gorgeous design, as shown below. Note the stamp for "Birdseye School District No. 32." I'm not sure where that was located, but one possibility is Birdseye, Indiana.
2. More illustrations by Lucille Enders are showcased on this Flickr page.
3. And here's a Flickr link to another Matilda Breuer illustration.