Both Claire Riley, 23, and her mum 56-year-old Susan Aucott pleaded guilty to offences related to the death of baby Molly-Mae Wotherspoon in Daventry in October 2014.
Molly-Mae was attacked by an American pitbull named Bruiser.
Jailing them both to two years behind bars, judge Justice Carr told the pair that Molly-Mae was savagely attacked by the pitbull in "a tragic and totally avoidable incident".
James House, the prosecutor, said the pitbull broke free from his cage in the kitchen and opened the door to the lounge to reach baby Molly-Mae on floor.
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It grabbed the six-month-old by her head.
Aucott threw herself across the baby but it was too late. Molly-Mae suffered injuries to every limb and puncture wounds to her brain.
She died from severe blood loss due to the head wounds, a post-mortem examination showed.
The American pitbull dog, a breed banned in the UK, was put down at the scene.
However, the baby's cries made it "an object of prey", the court heard.
A vet who treated the pitbull said Bruiser was was one of the most dangerous dogs she had seen.
In June, Aucott, of Alfred Street, Northampton, admitted being in charge of a dangerously out of control dog resulting in death.
She was jailed for two years but will be released on licence after one year. She was also banned from owning a dog for 10 years.
She was sentenced to two years, one of which she will serve in prison before being released on licence, and was banned from owning a dog for 10 years, the report said.