I'm in academia. And I married a collaborator.
In a situation like this, I think they're fine as far as ethics go. The relationship
started after the course ended, and the professor is not currently in a position supervising her. There's generally no official barrier about dating
between ranks or at the same rank, but the senior person should not be in a supervisory position (teaching, supervising, sitting on a thesis committee, evaluating proposals, writing references) and should excuse themselves from things like proposal evaluation committees or hiring discussions when their SO is being discussed. In the same department, they need to be a bit careful about passing information between levels - there's stuff that a faculty member hears about, for example, that a student isn't supposed to know.
However, I would also expect some gossip/eye rolling over the situation that will eventually fade The older male professor dating
a much younger female student/former student is a bit of a cliche in academia, sort of like the stereotype of a guy going through a mid life crisis, buying a sports car and going after girls half his age. If the professor and the student don't make a habit of this, the gossip will die down fairly soon, though.