Certainly you can use it. I think it lends emphasis for example it makes the question stronger: What are you doing John? Whatever are you doing John? suggests John is doing something odd or unusual. Whatever are you doing here? suggests you are surprised to see that person.

It is from an authorized text book.But I have never seen the usage before so I asking here.

I have only seen "whatever" used in a question when it's used in the sentence "Whatever do you mean?", which means the same as "What do you mean?" but with the implication that you are insulted or baffled by whatever was just said. I haven't seen it used the way you have used it.