The Bunny Tots Games and Amusements was published in 1928 by A.L. Burt Company. It's many stories and illustrations were originally seen in The Washington Post in Edward McCandlish's Sunday column. The books were written and illustrated by Edward McCandlish
The Bunny Tots did not only ride frogs. Here is an illustration of one saddling up on a squirrel. My father was most likely the model for this illustration