Is it an dad's place / business to ask his 23 year old daughter if she's still a virgin?

I would say that it depends on how the question was posed. Exactly as you stated? No. But, if it was a question like, Are you using protection? That is out of genuine concern for your welfare and not just busy body then that might be acceptable. Especially if you are living under his roof and support and the consequences of you not using protection might end up on his shoulders.