The Polish phrase does not start with "Czy" - it became a question only after a question mark was added, so the English translation should also have the same structure - no inversion. "You have a younger sister?" should be accepted.
"Czy" is not that needed, but a question without it can suggest that the person is not asking, but is surprised by learning that the interlocutor does have a younger sister. And so does the English sentence sound. (for both of them, a proper intonation would be important, obviously) Therefore it should be accepted, I guess.
Small tip: you wouldn't really use 'ona' here, it sounds as if you changed the subject :) It sounds like that:
- Do you have a younger sister? - Yes, her name is Jenny. - And is SHE (some other girl than Jenny) taken?