If it is so large that you actually would need to break it up, chances are you will not be able to do this yourself, as hardened stool is usually stone hard. You would have to use a lot of pressure and you would have to enter two fingers, which, as your daughter is only four is I think almost impossible.
If you feel sure enough to try it, then I would. Otherwise take the advice to go to an ER and have it done there.