13 And they were bringing children to him that he might touch them, and the disciples rebuked them. 14 But when Jesus saw it, he was indignant and said to them, “Let the children come to me; do not hinder them, for to such belongs the kingdom of God. 15 Truly, I say to you, whoever does not receive the kingdom of God like a child shall not enter it.” 16 And he took them in his arms and blessed them, laying his hands on them.
In this passage, we see Jesus rebuking the disciples for not permitting the children to come to him, for "to such belongs the kingdom of God." While I don't think I can argue from this passage that children of believers ought to be baptized, I think the passages leads to very strongly in that direction. The text is clear that not only "professing children" can be brought to Christ, but all children (or specifically, those of believers).
Who are these children? It seems clear (v. 13) that these were not just stray children that were wandering the streets, but rather children of those who actually believed in Christ (which is not to say that they were "saved", for it seems that such a term is fairly broad, see John 2:23-25, where many believe in Jesus, but He didn't believe in them).
What were the disciples rebuked for? They were rebuked for preventing the children from coming to Christ, or more specifically, rebuking the parents who were bringing their children. The children in this passage are wholly passive.
Why? Because they know nothing better. In fact, it would seem that they know little at all. It is without continually entertaining doubts and wandering away that they are brought. There's no where else for them to go! And for us, we must renounce all things, count it all as loss, and receive Christ, sometimes not even coming by ourselves but led by the hand or carried by the arms. That's why I see it as totally appropriate for parents to bring their children before Christ, calling upon Him to bless them, and trusting Christ that it is to "such as these" belong the Kingdom of God. Does that mean baptism? I think so, but that's another topic.