Her father Javed was seriously injured and police said he remains in a critical condition fighting for his life in hospital.
The grief-stricken family said Iman had a "special bond" with her cousin Aaima and her "last act in the world" was to free her from the vehicle.
The family's emotional statement read: "She was a beautiful, caring, fun-loving, inquisitive.
"Iman could play patiently for hours with her younger baby cousins but she could also tell you the impact Brexit had on the pound! She had her GSCEs planned and wanted to study medicine."
Her mother Khaldah described her as a "blessing from Allah".
The family, which also includes Iman's twin brother Rehan and older siblings Usman, 18, Mariyah, 19, and Sannia, 15, thanked the emergency services and the Royal Preston Hospital and Wythenshawe Hospital for the care given to Iman and her father.
Linda Cotton, headteacher of Iman's Norden Community Primary School in Rochdale, said: "We have all suffered a tremendous shock at the death, in such tragic circumstances."