Of course you should quit a terrible job, but leaving with such little notice is screwing them over because they will either have to cancel their vacation or find your replacement in a week. That's very unprofessional and pretty mean. However, if you don't need the reference and the job is unbearable, do what you need to do and deal with the consequences.
Then the MB should try treating her nannies with courtesy and respect. I'd bet a considerable amount of $$$$ that OP is just one of many nannies who have left with short notice. You owe her nothing, OP.
We don't disagree. Of course all MBs should treat their nannies with courtesy and respect. As I said, if OP's situation is unbearable, she should quit immediately. That said, it is also in the nanny's best interest to act professionally, especially if she needs the reference.