So where does the Soul of the child go if it dies 10 days after birth as my child did?
I cannot say definitively. I also lost my second child, so I wish to know as much as you do, but I cannot know. I can have "hope" and the knowledge that our God is a VERY GOOD God, who will do the best possible thing in accordance with His Word and His will, as long as neither cause Him to be a liar or one who looses some of His divine attributes.
We "know" that God cares about children:
1) He gave us children
2) He gave us laws and rules for dealing with children
3) While Christ walked the earth, Christ was sensitive to children and their needs, indicating that they should "come to Him" and that He would judge harshly those who hindered them.
4) We know that God's commands specifically deal with children and orphans (in regards to social care).
5) We know that God judged nations and peoples for their crimes against children.
6) We know that God told us via the Psalmist and others that He knew us while we were in the womb.
7) We know that David, a man after God's own heart, mourned his son while his son was sick, but once that son died, David proclaimed that his child would never return to him, but that he would to to where his child was.
8) We know that God caused at least one child in the womb to react to Christ (John the Baptist).
There may be other things that we "know" that I have inadvertently left off this ad hoc list.
What we don't know is "exactly" what it is that God does with children if they die before they make a profession of faith in Christ alone based on faith alone by God's grace alone as expressed by the Scriptures alone. We are simply never told, and we can argue until we are blue in the face and never resolve that issue.
But, we also know that all children are also in the class of people called "sinners." And as such, they would still need the efficacious power of the atonement of Christ in some manner, as do all people who are sinners (all people).