Cloey was a rear seat passenger in a northbound Nissan Tiida with her parents and sibling at the time of the crash.
"The occupants of both vehicles were wearing appropriate restraints and Cloey was in an approved and correctly fitted car seat," police said.
Witnesses told police the Faber-Thomas' car crossed the centre line as it left a bend south of St Andrews.
The driver and passenger of the southbound Nissan Terrano were taken to Timaru Hospital as a precaution and have since been discharged.
Cloey's parents have requested no condition updates be given.
Police today also released the names of two women who died after a two-car crash south of Auckland on Saturday.
Chinese nationals Na Huan, 22, and Zhuangya Xu, 23, were injured in the crash on State Highway 22 in Karaka, near the intersection with Blackridge Rd, about 6.40am.
One of the women died at the scene, while the other died during surgery at Middlemore Hospital.
The women, who were in New Zealand on working visas, had been travelling in a yellow Toyota Altezza with one other person, who police said was also a Chinese national.
He remained in hospital in a critical condition.
The two women were not believed to be related to each other.
The other vehicle involved in the crash was a white Toyota Altezza, which was travelling in the opposite direction on Karaka Road. Police said it appeared the white vehicle crossed the centre line. The driver of that vehicle also remained in hospital with serious injuries.
A police spokeswoman was unable to confirm the nationality of the driver.
Everyone involved in the crash had been wearing a seatbelt, police said.
