I'll make a short preface by saying that my personal opinion of any "punishment" in this case should be restricted to severe neglect on the part of the babysitter, and extensive counseling on the part of the 10-year-old to determine possible mental illness. It would also most likely be appropriate to apply various cognitive tests to see if the child in question has developed properly. Neurologically as well as socially.
It seems that the two big questions in this discussion is whether a ten-year-old child can distinguish right from wrong (moral development), and whether or not they can logically predict outcomes of their actions (cognitive development).
I apologize in advance: relevant wall of text incoming.
If we first consider the question of whether or not the child is capable of logical reasoning, we can examine the work of Jean Piaget and his ideas of stages of cognitive development in children. By the age of 6-12 children should have acquired the necessary cognitive ability to demonstrate effective planning towards an end goal, as well as show a marked decline in their egocentrism (the inability of a child to decenter form their own perspective and take on another's. E.g. a son who wants to get daddy an action figure for his birthday or maintains that the moon follows them around when walking out at night).
Gardner and Rogoff conducted a study in 1990 comparing the performance of groups of 4-6 year old children with groups of 7-10 year old children in a circular maze-puzzle. The children of 7-10 showed an ability to plan almost their entire moveset ahead of time to achieve the desired outcome, while the 4-6y.o. group could only plan ahead to a certain point from their startpoint and subsequently did poorly on the test in terms of number of errors made. There have also been studies involving children solving simple Tower of Hanoi problems (so they are good for something, who'd have thunk?) showing that children as young as 7 had ability to consider their actions logically in terms of reaching their desired goal with as few moves as possible before actually taking an action. (Klahr, 1989)
In conclusion, I believe that a child of 9 years should be able to logically asess that the outcome of shaking and throwing a baby would be harmful. I do not believe that the babysitter should have foreseen this behavior.
As for the moral development: Lawrence Kohlberg conducted studies from 1969 to the early 2000's presenting children to various ethical dilemmas and asking them whether the person involved was right or wrong to do as he did, explaining why they felt so. His most famous ethical dilemma is from 1969, is called the Heinz-dilemma, and should be familiar to most people (shortened here from original version):
"Heinz needs medicine for his dying wife, the only druggist who has the medicine charges ten times as much as it costs him to make it. Heinz goes to all the people he knows to raise the money, but can only raise about half. He offers the money he has to the druggist along with his story, but is turned away. Desperate, Heinz breaks into the store at night and steals the medicine for his wife, was he right to do so?"
Kohlberg constructed six moral stages from his results, and concluded that children reached what he called Stage 2 around the age of 7 or 8. Children at this age realize that people can have persepctives different from their own, sometimes even confilicting with them. Thus, they believe that what is morally right depends on the specific perspective of the person in the dilemma. This results in a belief that what is morally right is the action that serves one's own immediate interests and letting others do the same. Fairness is understood in the context of equal exchanges. Children at this stage might respond to the Heinz-dilemma that Heinz should steal the drug, since he would want his wife to do the same for him should he get sick himself.
Quoting directly from Cole, Cole and Lightfoot (2009): "Stage 2 (of Kohlbergs theory)is the key transition associated with school-age children's ability to get along without adult supervision."
Based on this, I can't say that 9-year-olds are entirely expected to perform properly around babies, but they definitely should be able to recognize that shaking and throwing a baby will not serve their own interest, and can be expected to be without supervision for short amounts of time. Keep in mind that we don't know everything about this case based on the rather short article provided. It is not uncommon for children that age to show small resentment towards younger siblings for various reasons, decreased parental attention for example. Most children do not react this violently to such percieved slights, however, especially not at this age.
On the basis of what I know of the case and the above: I do not believe the babysitter should be charged with anything beyond possibly neglect, depending on the circumstances. The 10-year-old should also be closely monitored for any pathological conditions, psychological or neurological. Not outrightly punished though, that would accomplish absolutely nothing, least of all any form of rehabilitation.
