"But the mum has had the presence of mind to reach out the window and grab the child to save her from going under the vehicle," the spokesperson said.
"It was quick thinking on her behalf, so hats off to her in that respect."
The girl was airlifted to Christchurch Hospital where it is understood she had surgery to insert pins into her legs.
While the mother was "distraught" when emergency services arrived, the girl was "almost a pleasure to deal with" given the pain she must have been in.
"To deal with as a patient she was actually fantastic. She was a lot easier to deal with than a lot of older patients with injuries that are less substantial then hers. She was very stoic and brave," he said.