This was the work of Sarah Noble Ives. From Wikipedia:
Sarah Noble Ives (March 1864 – November 1944) was an American author, illustrator, and historian known for her children's books including Dog Heroes of Many Lands and Songs of the Shining Way. Her work also appeared in publications like the New York Herald Tribune, the Boston Globe,[1] and McClure's, sometimes under the name Noble Ives. Later in her life she researched and published a history of Altadena, California.There's more information on her Wikipedia page. Here's an original of Little Bo-Peep I found at Heritage Auctions.