No, not like that, at least in a non-breeding context. You probably already know that answer to this, but the dog penis comes out when a dog is aroused. It’s shape is similar to the top of a rocket or lipstick, hence the nicknames for a dog penis.
“Red rocket” or “lipstick” is a pretty apt term: A dog’s erection generally ranges from pink to red in color, and is stiff as well. (That’s the furry area you thought was a dog’s penis in more innocent times.) Those terms describe a dog’s actual penis, which, for the most part, stays in the prepuce. Since we humans are uncomfortable with saying the “p” word, colloquial terms like “dog lipstick” or “red rocket” are popular substitutes for the term dog penis. Basic Terminology - What Exactly is a Red Rocket?
Warning - some photos ahead are graphic! A dog penis in prepuce.
