How is it proper to say, to doom smb to death or to doom smb to die?
Please be aware that I'm neither a native English speaker nor a teacher.
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.)
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.