Seven-year-old Emily Jones died after being attacked in front of her parents in Queens Park on Mothers Day last March.
Eltiona Skana was given an indefinite hospital order and jailed for life with a minimum term of ten years and eight months in December 2020.
The 31-year-old pleaded guilty to manslaughter by reason of diminished responsibility but was cleared of murder at Manchester’s Minshull Street Crown Court.
A Court of Appeal spokesman confirmed that Skana has been granted leave to appeal the sentence.
Skana – who suffers from severe paranoid schizophrenia – grabbed Emily and slashed her throat while the youngster rode her scooter through Queen’s Park, Bolton, on March 22 last year.
The 31-year-old, originally from Albania, was detained under the Mental Health Act.
Sentencing, Judge Mr Justice Wall said Skana will serve her sentence in prison if her mental health improves.