My school had very similar early readers, with very similar illustrations, but the characters were Jack and Janet, and their pets were named Tip and Mitten*. There was also a boy named Billy who had a pet goat. (Then again, EVERY vintage early reader textbook I've ever found has a boy name Billy who has a pet goat. EVERY. SINGLE. ONE.) The very first book in the Jack and Janet series was called Tip.
True fact: decades later I adopted a cat whose name is Tippy.
These were so sweet, and so not politically correct.
My brother, who was three years younger, got some new hifalutin' early reader called In the City ('Many many people live in the city.') This was bo politically correct; one of the stories was about the neighborhood kids getting together to turn the block into Puerto Rico so that their new neighbor Rosalita would feel at home. As you do.
*This was the eagerly anticipated sequel to Tip
By the by, both Fun with Dick and Jane, and Our New Friends will soon be available from my Etsy store: www.etsy.com/shop/PerpetualPaper