Then some children were brought to Him so that He might lay His hands on them and pray; and the disciples rebuked them. But Jesus said, Let the children alone, and do not hinder them from coming to Me; for the kingdom of heaven belongs to such as these. (Matthew 19:13-14)
And no, baptism is NEVER a work of man, it is 100% God's doing, and to call it otherwise is to not understand what a gift it is.
It's too important to take any chances by denying it to them. Jesus himself was baptised, and it wasn't because he "came of age" and suddenly figured out the difference between good and evil.
Baptism may be so, but to say that children HAVE to be baptized in order to be saved and go to Heaven, is ludicrous.