Kallum Aish, 18, was arrested in August after West Midlands Police released footage of the "distressing" incident in the Great Barr area.
Patricia Faulkner suffered a broken leg in the incident in Doe Bank Lane on July 22, and is still having difficulty walking.
Birmingham Magistrates' Court was told Aish, of Finchley Road, Kingstanding, Birmingham, was at the wheel of a Renault Clio which crashed off the road, hitting the victim and her Staffordshire bull terrier Millie.
CCTV footage released by police last summer showed the Clio crashing into undergrowth, before three young people emerge and leave the scene on foot.
Prosecutor Richard Purchase told the court on Thursday: "This is a matter that clearly should be sent to the Crown Court.
"I don't intend to play the footage. It essentially shows a very nasty collision between a car and a pedestrian and the pedestrian's dog.
"There are two cars going down a country lane – the second car loses control, swerving to the right, and the dog very sadly was killed."
Camera footage, which is graphic and could be distressing, was released by West Midlands Police:
The victim suffered a broken leg and needed stitches, Mr Purchase said, and had provided an emotional statement to police in relation to the loss of her eight-year-old pet.
Aish's solicitor told the court his client denied racing with another car at the time of the accident.
Mr Purchase said: "Whilst that it likely to make a difference to sentence, it would not be enough to keep the matter in this court and it should go up to the Crown Court for sentence.
"Having seen the footage, Miss Faulkner is very lucky to still be alive, having been hit by the car in that way.
"The eventual sentence will be far and away above the sentencing powers of this court."
Magistrates committed the case to Birmingham Crown Court after granting unconditional bail to Aish, who was given an interim driving ban.
Aish, who was ordered to appear at the higher court on February 25, also admitted failing to stop after an accident, driving without third party insurance, and driving other than in accordance with a licence.
He also pleaded guilty to criminal damage in relation to the death of the dog.