I remember reading this book as a kid in the early 1990s. It was Choose Your Own Adventure in style, but I don't know if it was actually CYOA brand.
From what I recall it was targeted towards middle grade reading. It sounds somewhat similar in concept to R. A. Montgomery's "Lost Dog!", but there's a big plot point missing in all the summaries I read online for that book: It turns out, depending on your choices, that you discover your "dog" is actually an alien from Sirius, and is a secret agent. This plot could lead to discovering that the "dog house" was actually a spaceship, and could travel back to Sirius.
Various other endings I remember included getting knocked out in an alley or something similar.
It was a paperback.