Not that rare, there are plenty of them (Tracey Andrews, Joanna Dehanney, Aileen Wuornos, etc). Here in England, we had Mary Bell, who, aged 11, accompanied by her friend 13-year old Norma Bell, deemed of subnormal intelligence, throttled to death three-year old Martin Brown and three-year old Brian Howe, as well as mutilating the latter's groin region and carving her initial "M" with a razor on his stomach. He was found covered in grass and some wild purple flowers (speedwell?).
When questioned by police, Mary finally claimed she'd seen a little boy in the street carrying some bent scissors and "covered in grass and little purple flowers".
She then became prime suspect. Compare and contrast Amanda's detailed claim of how "Patrick had sex with Mez and killed her, whilst I covered my ears as she screamed".
Mary was a sociopath due to her horrendous early childhood, with her mother repeatedly trying to kill her or give her away (feeding her pills, pushing her out a window, giving her to a childless woman, etc) and submitting her daughter, as a common prostitute, to paedophiles whilst a toddler.
If Amanda killed Mez, then I would feel fairly confident there is childhood abuse there in the background, as was the case with the James Bulger child killers, Venables and Thompson.