I think while it is true that all have sinned and fallen short of the Glory of God, I would like to point something out that was pointed out to me and this is just another thought, Reguarding Romans Scripture, could it be possible that in the context, Pual is being asked who is the greater sinners, those who are without the law and those under the law, Paul says it makes no difference " All have sinned and fallen short of the Glory of God "..Talking about the Jews and Gentiles..?
As for babies being sinners, well as katz has mentioned what sin has a baby committed, None..what is the meaning of sin ? well I believe it to mean when we transgress against Gods Laws, until then we are not guilty of sin until we commit it. Paul said
" Indeed I would not have known what sin was except through the law. For I would not have known what coveting really was if the law had not said, "Do not covet."[2] 8 But sin, seizing the opportunity afforded by the commandment, produced in me every kind of covetous desire. For apart from law, sin is dead. 9Once I was alive apart from law; but when the commandment came, sin sprang to life and I died.
Going from what Paul has said, he didn't know what sin was until the law came and told him he was sinning, when he knew that he was sining that was when he died [ spiritually ] . So like a baby until he/she knows right from wrong and realizes that He/She has comminted sins and in need of a savior then where has a sin taken place..