All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
If it is proved that the housemaid killed that child intentionally and the kin of the victim refused to pardon her nor accept Diyah (blood money), then she has to be executed in retribution. Allaah The Almighty says (what means): {And do not kill the soul which Allaah has forbidden, except by right. And whoever is killed unjustly - We have given his heir authority, but let him not exceed limits in [the matter of] taking life. Indeed, he has been supported [by the law].} [Quran 17:33]
However, determining the type of that killing, i.e. whether it is unintentional or intentional or quasi-intentional is to be done by courts for they examine the facts and question the parties of the dispute and give the suitable judgment. In an incident such as this one, Fatwa is of no avail.
Allaah Knows best.