Carl Baxter, 36, smashed into Emily Kerwin and her father, Stephen, who were on a bike and trailer, after Mr Kerwin remonstrated with him for driving too close to them, Hull Crown Court heard.
Emily lost five teeth and suffered fractures to her face and palate, in the incident on the A1034 at Newbald, East Yorkshire.
Stephen Kerwin, 52, suffered a broken leg and pelvis and still has a metal leg brace.
"
He used the car as a weapon - this is what is commonly known as a road rage attack
"
Simon Keely, prosecuting
Baxter, a chemical engineer, of Shipton Road, Market Weighton, East Yorkshire, stopped his car and reversed 200 yards at high speed after Mr Kerwin shook his fist at him, the court was told.
The trailer was crushed under the rear wheels of the vehicle and Emily was found by paramedics hanging upside down by the straps in her buggy.
Baxter fled the scene, but later returned as police and ambulance services helped the father and daughter.
Apology offered
Prosecuting, Simon Keely told the court: "He used the car as a weapon to cause injury. This is what is commonly known as a road rage attack."
Baxter pleaded guilty to dangerous driving, two charges of causing grievous bodily harm, and one count of leaving the scene of an accident.
Sentencing was adjourned pending a report from Humberside probation service.
Speaking outside the court after the hearing, Baxter said he had not realised there was a child in the trailer.
"I would give anything for it not to have happened. I want to apologise to the family."