Like you said you are both adults so I can't see any morale dilemma. As she is not your student you can't be accused of some how using your position as her teacher in any sinister way (whatever that might be). The university bosses probably won't care so long as you're not rubbing it in their faces. What you'd have to be careful of is if they are looking to get rid of you then this is just the kind of thing that your fao or other management will hold against you.