An unbaptized baby is justified in the sense that they are free from PERSONAL mortal sin, though still stained with Original Sin. A person who dies after desiring Baptism, but before receiving the remission of Original Sin through the sacrament, is in the same condition...in theory.
No, there is a huge difference between an unbaptized baby and an adult justified though BOD. The adult is justified, and has sanctifying grace. The state of sanctifying grace is uncertain (contra certain Protestant beliefs) but if it is granted that some adult died justified via BOD, then we should expect eternal reward for that adult.
I am aware that since V2, some speculate aborted babies get a BOB. Let's just consider only an ordinary baby who dies without baptism. In standard pre-V2 theology, that baby is not justified and is not in a state of grace.