If it's an otherwise healthy child who has yet to take a breath, that means the doctors have yet to get their lungs stimulated so that they can take a breath. I would expect a doctor to work as long and as hard as they could to save the life until there is no hope.
At the point there is no hope and the child is stillborn, then, if the woman wanted to donate their child's organs to help other children, she should have that right if she wants it, because the relatives of old people on life support have that option.
Do you even read what you write? You expect a doctor to "save the [child's] life," but you deny that the child is a human being until its starts breathing. What if the doctor decides to do nothing and lets the child die? Should that be legal?
Do you understand the definition of "stillborn?" It means the "child" has already died (no heartbeat) in the womb, not that it failed to maintain viability after delivery.