Kallum Aish, then 17, was at the wheel of a Renault Clio when he lost control, hitting Patricia Faulkner and her Staffordshire bull terrier Millie, in Great Barr on July 22, 2020.
He later admitted six offences – causing serious injury by dangerous driving, criminal damage, failing to stop after a crash, driving while unlicensed, uninsured, and possession of cannabis.
The incident involving Ms Faulkner happened in Doe Bank Lane, Great Barr, throwing her over a hedge and leaving her badly injured.
She was left with a broken leg and concussion, while Millie was killed instantly.
Shocking CCTV footage of the crash was released in the aftermath by police as part of an appeal for information.
It showed the blue Renault losing control in a cloud of tyre smoke, then crossing the carriageway, hitting Ms Faulkner on the opposite side of the road, before disappearing into undergrowth.
Aish's sentencing was delayed last year after he was knocked off his bicycle by a car.
But the 20-year-old, of Cattell Drive, in Sutton Coldfield, was sentenced at Birmingham Crown Court yesterday to 22 months in a young offender institution, suspended for 18 months.
He was also banned from driving for three years and ordered to carry out 30 days of rehabilitation activity.
The court reportedly heard that Aish was speeding and had been racing someone at the time of the incident.