I voted no only because I think street photography is more one of capturing moments as they occur, with the photographer merely a lucky observer in the right place at the right time outside of a dynamic setting looking in; so street photography is IMO, about both the setting and the people in it, going about their lives, most of them are unaware of the camera.
This is more of an impromptu portrait. The difference is, this subject is aware of you, and engaging you and the camera, (so is the dog), so the photographer is now part of the dynamic.
While this is not a portrait per se, this photograph is about the woman, and the things she wears, her cigarette, her dog, are clues to her personality.
As such it's good picture, you could make a photoessay of her and her dog and her day, and it would be interesting.
Last, since she did say you could photograph her, consider how you could have composed the shot. I usually see where I should have stood in relationship to the subject while I'm reviewing my shots on the computer
. I get so intent on the main subject that I don't notice the clutter or angles. The foreground and subject colors are good.