While the other answers are already perfect, I'd like to add a thing.
I will undergo a fertility surgery next year. I will be out of office for likely one week. Of course the surgery of your colleague can be anything, but I just want to tell you the implications of "my" type of surgery.
Of course I know about the one week sick leave beforehand and I find it only fair enough for my colleagues to share the information as soon as I know the exact date. I would feel playing foul not telling them beforehand. They are planning with my work's results and our meetings, of course, and they will have to reschedule lots of things if I don't tell them beforehand. So I will cause them lots of avoidable extra work by not informing them in time. So I'd love to tell them, hey guys, I'll have some surgery planned next week, I won't be available.
I would definitely hate to be asked what the surgery is for, though.
Fertility surgery hints on me trying to become pregnant. Which has - of course - huge impact on my working ability. If it works, I will most certainly need some weeks of sick leave due to pregnancy issues, and of course parental leave. In Germany, where I'm located, I'm allowed to leave up to three years! (which I don't intend to, but my colleagues can't know my plans - and I would definitely be allowed to lie about them according to German law if they asked, so they can never be sure how long I might be away)
Of course this can have huge impact on me being considered for raises or promotions.
Therefore, I'm not interested in telling them anything. I have surgery. No more information.
I'm planning to tell them about my planned surgery as soon as I know the concrete day, yes. But if they ask for further details, I will not tell them. And if they don't relent in asking, it will be the first and the last time ever I will have told them.
So, if you follow up, you risk to never be informed beforehand again. She will just call in sick the day of the surgery the next time.
So far, she is being very fair in telling you everything you need to know right now. Don't ask for more.