I mean, at what point is one supposed to suddenly question and be suspicious of meds their parents and doctors have had them on, since forever? That would be paranoid :'p
I assume from context that the father feels bad for her and wants her to be happy to some extent, but also wants her to stay out of the lime-light (for who-knows-what reasons good or ill on his part, and whatever the Temple has to do with them) ...and everyone knows the Duke is likely to notice what's up sooner or later. Sooner, now, of course.