I've been asked this many times over the years and I must confess at the outset that the Bible does not specifically cover this question. But I have talked to dozens of believers over the years who consented to be baptized when they were children, and who after making a decision to walk with the Lord as an adult desired to be re-baptized as an expression of their commitment. Personally I see nothing wrong with it. In fact, if a believer feels compelled to repeat baptism as an adult I think it's a great thing to do.
To be honest, I don't really like baptizing children. I'll do it, if a parent is involved and assures me the child understands what they're doing, but overall I would really rather not. Kids just don't possess the maturity to make a solid and cognizant decision to follow Christ, and I think baptism should be reserved for whenever that decision is made with the adult understanding of what that commitment entails. What a child generally can't understand is the cost of following Jesus—something our Lord brought up repeatedly during His public ministry and wanted people to be aware of.
I certainly love the statement by our Lord to "let the little children come" to Him and we should certainly never hinder them. But I've dealt with so many adults who grew up to regret being baptized earlier in life that I am now of the opinion it's better to wait. But once again, that's just my opinion.