After agonizing over their choice of pet for ages, the narrator finally comes to a decision at the end of the book. He says:

The dog…? Or the rabbit…?
The fish…? Or the cat…?
I picked one out fast,
and then that was that. (26.5-8)

And that's that. We don't get to see what pet he picks, or even which ones he dismisses outright. We don't know if the kids go home with a dog, or a cat, or a rat, or a yent. There are no clues—the narrator just states that he's made a choice ("fast") and that they're going home.

The abruptness of the ending reveals that the pet itself doesn't really matter after all. The act of choosing is what the story's all about.