The babysitter should be charged for not taking care of the children. It was her job to take care of both children. She left an unsupervised baby with a 10 year old, an age at which legally you are not responsible for your actions. She's not a teenager, she's a child that pretty much does not discern from good, bad and everything in between unless told. She should not be charged with murder at an age where your mind is still growing.
Let me put it in another way. How many times as a teenager have you reflected back on your childhood and thought "man, I was stupid!". The same way this girl will look at her past self, except she won't think "man, I was stupid!", she'll probably consider suicide for taking another humans life unless she has some sort of mental illness. You're pretty much a different person every year until you become a teenager, an age where these "changes" tend to occur less frequently.
I feel sorry for the child. This stain will remain on her record for life, make it impossible to get a job or hell, live her life because of something she did at a point where the concept of counciousness was not present. She should be consulted by a psychiatrist and a physician to rule out any serious mental or physical illnesses that could have lead to this. A criminal record will do nothing to "rehabilitate" her. In fact, it WILL lead to suicide.
She needs counseling, not third degree murder charges. This was an accident.
EDIT:
In fact, I believe anything a person does well up until his 20's is accidental. A child's mind is to feeble to discern when it has done something wrong. Their sense of morality comes from someone else, usually the parents but they are easily influenced. By the time a person reaches teenagehood and they can actually discern from what is acceptable and what is not and at the same time use logic when making decisions their mind is extremely subsceptible to social influences. A teen who has done something that is considered "wrong" should be helped, not punished. In fact, this goes for every person who does not posses a mental illness. You can claim that once you legally become an adult you should discern from right and wrong but that's not true. Punishing a child for doing something they don't understand is wrong.
In fact, every single violent human behavior is due to negative influences during their early years.