I don't think the original is quite correct. Try, in past time:
Were it not for the doctor's urgent operation, the baby couldn't have survived.
or, even better, showing more clearly the sequence of actions:
Had it not BEEN for the doctor's urgent operation, the baby couldn't have survived.
Forget about classifications (conditional 1, etc).
Learn the correct ones by listening to their flow.
We have a contrary-to-fact situation in the above, and that normally requires "have" in the 2nd part.