5 month old in jogging stroller?

We have a 5 month old who can sit without support for extended periods of time (10 plus minutes). She is quite petite, 25 inches long and 13.5 pounds. Would it be safe to get a jogging stroller and go running with her? I think she would like the speed but it seems like a lot of bouncing. Do you know of any children getting injured by jogging strollers?