군요 is okay as a phrase indicating a discovery of some fact, but 하군요 is not grammatically correct. It cannot attach to a verb stem directly. The correct forms are 하는군요 (present), 했군요 (past / present perfect), 할 것이군요/거군요 (future). For adjectives, it attaches to the stem directly, as in 좋군요, 아름답군요, etc.
The sentence can be better phrased like this:
아 목요일은 안 되는군요. 네 알겠*습니다. 그러면 토요일 9시는 (or 9시에는) 괜찮나요? 아니면 시간도 바꿔야 하나요?
못 하는군요 can only work in some specific cases because 하다 denotes "doing" something. (안) 되다 expresses something works out or not, so it's a better choice for talking about possible appointment times.
Similarly, 괜찮다 is like "is okay/fine", so it can be used in any context where something is okay or not. 괜찮나요? (Is it okay?) is using the same -나요 ending you used in 하나요.