Girlfriend with a sharp tongue?

Anonymous
So my new girlfriend (we only officially met last week, although we'd seen each other out and about for a while) doesn't exactly mince her words at the worst of times. She obviously has the many character traits that attract me too her, and is also hot as hell, however in just over a week's time I've noticed that she can be moody when she doesn't get her way (she got quite grumpy on our first date and apologised the next day), and told me to fuck off on Facebook Messenger today when I jokingly told her to calm down (with emoticon attached- 😛) about something. I can be sarcastic but I'm very easy-going and soft-spoken. My questions are:

Might we be a bad fit for each other? Do these sort of relationships usually fail? There's no way I'll ever become a man whose other half berates him and take to him like he's sh**, so what do you think I can/should do about this? It would a shame to have to end this thing so early in, but I've never had a girlfriend speak to me like she does before!
Girlfriend with a sharp tongue?
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