Echoing what others have said here,
There is original sin, which we all are conceived with thanks to the fall of man...and then there is personal sin which is what we do. Babies are incapable of personal sin, though they are regarded as sinner by default due to original sin.
Young children who haven't yet developed understanding and reason do not have personal sin. My cousin, who is 19-years-old now and severely autistic, has not developed the same understanding even a 5-year-old has, and so I'm not sure I can count him as having personal sin either. Though he was born with the stain of original sin.
Yes but not by this worthy of condemnation...we sin because we are sinners not are sinners because we sin. Babies are by nature sinners and thus will at one time when a bit older (but still very young) commit sin, but but they are not held responsible to pay the penalty for the sin Adam committed. Our sin separates us from God, not someone else's, before then they are not separate from God.