You can. You can also say "What is your boy preparing?" (this is another meaning of "готовить", not related to cooking)
In fact, I would translate 'what does the boy cook' as 'что умеет готовить (literally what can he cook)', and 'что готовит' as 'what is he preparing/making'.
In English, there are two usual meaning differences which can be ascribe to "What does your boy cook?" The first meaning is the equivalent of the present progressive "What is your boy cooking?" which includes the unspoken [at the moment/right now[. The second refers to capability and/or knowledge OR to habitual action. While your boy may or may not be cooking right now, what does he know how to cook - what does he cook when he cooks? OR what does he cook when he prepares breakfast for his family?
For example, I have a friend with extremely limited cooking skills. If he is asked to prepare something hot to eat, the only thing I have ever known him to cook is macaroni & cheese (from a prepared and measured box of both) mixed with Tuna fish (from a can). He knows how to boil water, time the pasta while it cooks, open a can of Tuna fish and drain it, and mix everything together when the pasta is cooked. So, what does he cook? He cooks the meal I just described. It's really not bad. Not good, but not bad.
So, does готовить refer to this kind of capability/familiarity/habitual element of the English verb, or does it just mean "prepare/cook/make" at the moment?
Many English verbs can be viewed in this dual or triple way. Is Russian more particular, or does it allow to the same treatment - or something different?