Anyone, anywhere can ask you anything at all but you do not have to answer. If you are threatened for not answering, that is a different thing. Why are you worried about this now?

If you don't want to say much, just let them know you are taking time off for a "doctor's appointment". They may request a note from the doctor or something, there are old fashioned places like that but they are usually bigger where people abuse their sick leave or whatever. I doubt they will say much of anything except, since it is such a small/close office, maybe they will be concerned you are "sick" and want personal reassurance in a good way that you are fine (not in pain or worried or that they might be able to help in some way) so maybe I'd just say a "routine doctor's appointment". I liked when I worked part-time because it was easier to schedule things when I wasn't due to work so I didn't have to think what to say as I didn't have to say anything at all.

If you have a problem though, it can get worse if your employer is clueless; no one likes to be "surprised" and if you haven't told them anything they can't be required to help/accommodate; it can be a two-edged sword. But, in such a small office, everything is more personal and less official anyway (they are not big enough for many laws to apply) and it gets to a he said/she said sort of situation which is hard to prove wrongdoing for.