If your job duties are expected to have any overlap at all, I think it's reasonable and uncontroversial to veto the hiring of someone you know you aren't going to be able to work with productively. So that's a starting point.

But if there's no expected overlap in duties and you just don't like the idea of her being in the same office, it seems to me that that's not really a professional issue anymore. It's a personal problem. (There's nothing wrong with having personal problems, everyone's got some.)

It is a little unethical to negatively impact someone's career due to a personal problem you have with them, I'd say. But if changing your feelings isn't an option, it's hard to see that you have a choice other than telling your employer about your problem and suggesting a no-hire.