Beatrice Mawamba, aged 34, panicked and careered down a narrow alleyway into a grassed courtyard while taking a lesson with her husband, Leeds Crown Court heard.
The court was told she crushed to death nine-year-old Shamirah Grant and injured two other girls, one seriously.
The court was told Mawamba had a provisional licence but had only done online theory lessons and had not driven a car before.
Michael Smith, prosecuting, said: “The man was giving some sort of instruction to the woman. The children heard the engine revving and saw it stutter and come flying down towards them fast.”
The Vauxhall was earlier described as “bunny hopping” before Mawamba lost control and veered dangerously out of control, down the steps of the narrow alleyway and on to the grassed children’s play area near Leopold Grove in the Chapeltown area of Leeds.
“The defendant described the car going very fast and her husband telling her to brake but she did not know how to. Her husband also tried to stop the car but couldn’t.
“When challenged by the police she was unable to say which pedal was the brake,” Mr Smith said.
The court heard she was not travelling at speed during the incident and had only managed to get into first gear.
Sentencing, Mr Justice Openshaw said Mawamba was “profoundly ignorant” of the most basic driving skills.
The judge said setting off driving while “so lacking the most basic driving skills” amounted to a “thoughtless disregard for the safety of others”.
“In my judgment a prison sentence is necessary to impress upon others that driving a car without having any idea how to control it is seriously anti-social and presents a substantial risk to the public.”
Mawamba had admitted causing death by dangerous driving in May this year.
She was banned from driving for five years and must take an extended test when her ban ends.
In a statement, the girl’s parents, Gary and Jennifer Grant, said they had forgiven Mawamba and her husband.
“We appreciate that such a terrible event was not intentional,” they said.
“We have not sought to influence the sentencing of the court in any way.”