Since we know nothing about this little girl and her circumstances, I think it's extremely unfair to call her a psychopath. For a start, all personality disorders, including antisocial personality disorder cannot be diagnosed until 18 (although obviously signs start before that) due to the fact that children's personalities are still developing, and while all people with APD display psychopathic behaviour as children, not all children who display said behaviour go on to have APD. so no, she isn't a psychopath, she's a child who is still developing cognitively and more likely than not won't repeat this behaviour if she is given the help she needs. While I was still in uni working on getting my degree, we went to a centre that dealt with children who had committed sexual offences against other children, sometimes there were extremely violent, and had occurred on multiple occasions, and according to the women who run the program not one child who completed their program went on to become adult offenders. Child offenders are not the same as adult offenders, and more often than not do not go on to become adult offenders if they receive specialised intervention.
Also we don't know why this child was in foster care, and there could be any number of reasons that explain her behaviour. She could have developmental delays. She could be suffering from PTSD.
Since we're speculating I want to put a situation forward for you. Foster mum is outside and clearly out of ear shot of the baby, little girl goes inside for whatever reason, and hears the baby crying. Maybe she has younger siblings and is used to being in a care taker role to some extent due to a neglectful situation so she goes to try and sooth him, picks him up and drops him. Maybe in her previous home her punishments were severe, and she, as she said herself, panics, and literally the only thing on her mind is that this baby needs to stop crying or she's going to be punished, and she does something absolutely horrific, and inexcusable. But that isn't a sense of right or wrong, it's self preservation. Fear of punishment does not always equate to an understanding of what is right and what is wrong, especially with children who have been punished for even the most minor transgressions
She should not, regardless of the circumstances, be subjected to a trial as an adult. Even if she straight up murdered this little boy for no reason, she's a CHILD and should be dealt with in the juvenile system. Where would the sense be in making her sit through a trial, and risk damaging her psyche worse than it clearly already is. I'm not saying she should get a slap on the risk, she killed a baby, and it's important that that is remembered, but the best thing that can be done in this situation is specialised therapeutic intervention, not an adult trial.