The first several years of the life of a human, and perhaps considerably more than that in the more long lived humanoids, a child is unable to truly hold beliefs regarding morality and is necessarily neutral. What happens to the souls of those who die while still a young child? The easiest response is that they go to the Outlands like any other neutral being; but considering the frequency of infant mortality in the historical societies that the societies of fantasy worlds are based off of, we can be sure that the Outlands would be heavily inhabited; considerably more inhabited than canon sources indicate it to be. It is entirely feasible that they become petitioners in the Hinterlands (which would certainly add it the strangeness of the Hinterlands); but does anyone else have any theories?
And what of the extremely young infants? Before a child is one or perhaps two years old its intelligence, by my reckoning, is below 3. What of these individuals? Oblivion? If it is oblivion this would indicate that they don't have souls; if they don't have souls why is it evil to kill them? If it is evil because they will eventually have souls wouldn't it also be the case that it will eventually be evil to kill them?
These questions come partly because of a portion of a my campaign where/when the Illithids and Baatezu will be using children as human shields. But also from my aimless morbid ponderings.
If they were too young to have any particular beliefs, it could be that their souls simply drift, lost, in the Astral Plane, unable to form a connection with even neutral outer planes. Beings like devourers might find them and harvest them. Astral devas might scour the void, collecting them and bringing them to the Upper Planes.
Some might become ghosts or other forms of undead, if their deaths were traumatic.
If (either of) their parents were religious, proper funeral ceremonies should be able to send them safely to their parents' gods. Worshippers of the Greek Pantheon would know that children would end up in the realm of Hades like most everyone else. The Aztec pantheon has a special heaven set up for the souls of children.
Zaphkiel of Mount Celestia makes it his business to look after child souls, though he would presumedly have to rely on astral devas and trumpet archons to find them.