It's highly rude of her or she's just plain clueless to suggest such an expensive restaurant, whether it be your first date or a date after 4 months, if you're expected to pay, or even if going dutch. Why do you think it would be polite and the only thing to do, just because she is the woman? She's not being polite.
As a woman actively dating (although older than you) I would never suggest an expensive restaurant to a man I just met. And I seek out men who are accomplished because intelligence turns me on.