The pair were waiting to board a bus when the incident occurred.
Eye-witnesses say the vehicle, a black Toyota Caldina, was traveling westward, but at a very high speed.
It first hit the back of a car, before veering off the road and hitting the woman and her daughter.
They were rushed to hospital, suffering from minor body injuries and trauma.
Police attended the scene and the driver was taken for questioning.
By LACHLAN S. EDDIE