1. God sent His Son to suffer and die on the cross, so that children (among others) may rejoice in heaven, free of all sickness, pain, or death. It is not God's will that little children perish everlastingly (Matthew 18:14). They die physically because of Adam's unique original sin, and Adam's sin made us all sinful by nature (Romans 5:18).
But God judges individuals based on their works (Revelation 20:13), and babies have no works (Romans 9:11), so they are not judged. God cannot be accused of not caring about the children of the world. In one case in the Old Testament He refrained from judging an entire city, because of the children and animals that lived there (Jonah 4:11). God is also clear that He finds no enjoyment in punishing (Ezekiel 18:23). God made sure there was an open door to Heaven for all infants and children who cannot know Him or His moral laws. God opened that door with the key of the cross.
2. God visits the consequences of the sins of parents on their descendents (Exodus 20:5). Not the guilt -- God in Ezekiel 18 says He doesn't blame children for their parents' sins. But the practical consequences of adult wrongdoing cascade down on children. We see this in everyday life: when the court system jails a criminal, the punishment negatively impacts the children of the criminal.
A parent can bring divine blessing or cursing upon his or her own children. An example of blessing was Phinehas. When Phinehas righteously executed a rebellious Israelite with a spear, God rewarded his whole line with the honor of perpetual priesthood (Numbers 25:6-13). Another example is Noah -- we all benefit from Noah's obedience (Gen. 9:11). This principle ought to make parents tread more carefully. The Amorites of Canaan lived in violent, evil perversion for centuries, until God decided to erase them. They brought annihilation of their people down upon their own heads.
3. God is the only God, and the Creator, which gives Him absolute, unique rights that no human being has. No one may say to the Creator, "Who do You think you are?" or "What do you think You're doing!?" According to certain science/ecology websites, about 150,000+ people die each day. In each case, the circumstances of the person's death was ordained by God.
God alone decides how long each person lives (Psalm 139:16). Skeptics complain that God was "wrong" to have the Jews kill the Canaanite children. But, since God ordered them to do it, it was therefore not wrong. God always has the right to end life. God is not a giant man. If the Jews had done it on their own, it would have been genocide. But God through His prophet Moses ordered them to do it, so it was a divine judgment.
God is not a moral monster, because human beings do not have a right to stay alive a certain amount of time, or to die in a certain kind of way. There is no moral law, whether above God's head or created by humans here on earth,by which He may be judged. In addition, God created Heaven at the cost of His son's death, so that all the suffering of this life could be wiped out forever. God the Son knows exactly what it feels like to suffer horribly and die, so no one can accuse Him of apathy, and He came of His own free will to undo earth's suffering, so no one can accuse Him of indifference.