Is it ethical to date a graduate student of the same university where you are a faculty member?
I hope it's ethical!  (My husband was a graduate student at the university I'm a professor at, in a different department in the same school, when we started dating.)

The core ethical issue in faculty/student relationships is the power dynamic: it creates an ethical problem if you have power over her career, either in a way that could favor her (leading to concerns about favoritism) or disfavor her (leading to concerns about coercion).

In separate departments, that's not likely to be an issue: most assistant professors at most universities don't have power over graduate students in other departments.  There are still situations where issues could arise - say, if you ended up on the panel choosing which grad student from the school would win a prize, and she were a candidate; or if you were asked to be the outside member of her thesis committee (at a school which picks outside members to be professors from other departments).

So, unless your school has a specific policy on the subject, it's probably ethical, as long as you make sure to avoid being in a position that creates a specific conflict.