This is from a short address I gave on what happens when babies die?
What happens when an infant dies? That child stands before the Lord with glory and honor as a joint heir of Christ. How can I say this? Because God is good and Christ died for sinners. The 19th Century Princeton theologian, Charles Hodge explained in his Systematic Theology: “[A]ccording to the common doctrine of evangelical Protestants  all who die in infancy are saved.”
Hodge explains that the death of Christ, according to Romans 5:18-19, undoes the work of death wrought by Adam:
We have no right to put any limit on these general terms, except what the Bible itself places on them. The Scriptures nowhere exclude any class of infants, baptized or unbaptized, born in Christian or in heathen lands, from the benefits of the redemption of Christ.
In short, Jesus saves infants.
This doctrine is quite dear to me. At nine months of age, my first son died. He had a seizure late at night, then his heart stopped and his breathing stopped. He died while his mother held him. The paramedics came, and despite their best efforts, his heart would not start again. A few hours later, as the sun came-up, a man came to our house and laid a sheet on the floor of my son’s bedroom. He took the body of myson, laid him in the middle of the cloth and wrapped him like a package and then carried him away.