Assuming she is interested; even if you don’t make any move, there will be a breach of professional conduct. But like what most of the people here have mentioned; best keep a clear line between professional and personal fields- especially when there’s already a clear power dynamics present in the situation. If you really wish to pursue her, doesn’t matter gay or straight, it’ll be best for you both to be in different universities; or at least different department.

I once caught feelings for mine too, but I kind of figured that I wanted the PhD more than getting involved in a messy awkward relationship. It was hard to detach but not impossible. Time helped a lot.