have not heard 'What are you busy about?' before and find it unnatural.
are you busy with?' as in 'What are you busy with this morning?' is
fine as a question, but I don't think you would repeat busy with
in your reply. Instead, if you were a university lecturer, you might
say: 'Oh, I've got so much to do. I've got essays to mark and reports
to write and then I've got to go to the Dean's reception before lunch!'
often use busy directly with the present participle, as in:
'I was busy ironing when Jeremy arrived.' No preposition is then required.