Yes, I certainly believe we should encourage our children to give their lives to Jesus. My own wife believed in Christ almost as long as she could remember, and some of our own children opened their hearts to Jesus while they were still very young, and are still following Him today.
We shouldn't force them or demand they profess a faith in Christ, of course; that could lead to an insincere or false commitment that won't last. But God can work in their hearts just as much as He can in ours, and even if they don't understand everything there is to know about Jesus, they still can understand that God loves them and wants them to love Him in return.
Jesus said, "Let the little children come to me, and do not hinder them, for the kingdom of God belongs to such as these" (Mark 10:14). Remember, too, that as time goes by they won't remain children physically -- nor should they remain children spiritually. Teach your children to pray; read the Bible to them (perhaps from a Bible story book designed for children); take them to church. Above all, strengthen your own relationship with Christ, and help them see that Christ is important to you.
I urge you also to pray for your brother, and urge him to face his own need of God. As they grow older, many people decide they don't need God any longer -- but they do. The Bible says, "Seek the Lord while he may be found" (Isaiah 55:6).