Yes, the nurse screwed up and if the child had died or suffered some lifeterm disalibilty I might be more inclined to agree with you in this particular case what benefit is it to anyone to dismiss her ? This wasn't deliberate, it was human error and IMHO a severe reprimand with additional training would be a better solution.
Medical malpratice happens all the time - are we going to sack every single practioner for every mistake they make ?
I agree a large compensation package should be negociated - Fines tend to focus the minds of those in charge to improve conditions and safety standards