When someone asks "Do you know if..." the person is NOT wondering whether you actually know. If you don't know, you say so. If you do know, you don't just say "Yes, I do know that." You also usually omit saying that you do know, because by giving the answer, you have clearly shown that you know.
Either say you don't know, or just answer the question.
A: Do you know what time it is?
B: Yes, I do. --- This is an unacceptable answer by courtesy, regardless of grammar.
B: No, I'm sorry, I don't. -- This is fine. You can't give information you don't have.
B: It's 5:10 pm. Sure, it's 5:10 pm. Yes, it's 5:10 pm. -- You can say "Yes" or "Sure" but you don't say "Yes, I do know."
So in your example, it's completely unnatural to say "Yes, I do."