M.M.
They older they get, the harder it is to train, since they have their own little minds.
I have done CIO with my 3yr countless times. Infant, then 17mos, then 23mos, then just recently at Christmas time.
It's always because we create a habit - path of least resistance - and then we have to undo it.
You can definitely do it at her age, and you may have to do it several more times as she continues to teethe and get sick.
For us, at his age, it's the only thing we can do. He needs to understand that temper tantrums do not get him what he wants...which is basically what's happening with the screaming at night for you. She cries,and you go. If you don't, she'll be mad, but she'll be fine.