Absolutely not. It would make no sense.
Why not use the money and purchase a small token of appreciation for the teacher and assistants/helpers at the new daycare where your child attends now?
This. It makes no sense to give a bonus to someone who doesn't work for you anymore. If you had wanted to give her a bonus, when she left would have been the time to do it.
You aren't responsible for making up her expected bonus because she changed jobs. I'm sure she is not expecting you to, if she is a professional nanny.