She was struck by a grey Hyundai at Irvine Park in the town shortly after 17:00 BST on Thursday.
A spokesperson for the Northern Ireland Ambulance Service said two off-duty nurses tried to help the girl, along with paramedics.
She was taken to the Ulster hospital by ambulance but died from her injuries.
The driver of the car is helping the police with their inquiries.
Police have appealed for witnesses to contact them on the non-emergency number 101.
A girl who died after she was hit by a car in Bangor, County Down, has been named as five-year-old Katie Grace Bogle.