There have been several studies indicating that the neocortex is the part of the brain responsible for self-awareness. People with a lesion on the Visual 1 section of their cortex are "blind" but if you toss a ball at them they'll catch it. And if you have them walk through an obstacle-laden hallway, they'll avoid all obstacles, but be completely unaware of having done so. They can see, but are unaware of their own sight. So I would say the point at which a baby cannot be euthanized is dependent on the state of their neocortex. Further study needs to be done to determine that point, but I would say by two years old the neocortex is highly developed.