I always thought that "to comdemn to death" sounded more like a decision of a court. My context here can be rendered in these few words: "We can't leave this child here and doom it to die/death".
We can't leave this child here. We would be sending him to his doom.
We can't leave this child here to die.
We can't leave this child to its fate.
We can't leave this child here. We would be dooming it to die.
(The last example is my least favourite and I think the least natural.)