"What are you doing this week?"
Translation:Mit csinálsz a héten?
So, I wonder how general you want to go here. Are you still thinking about this week, just don't want to emphasize it? In that case, "Mit csinálsz a héten?" works just fine.
The other option would be just any week. But then, all the days in the world are part of a week somewhere, right? :) So, then, I'm guessing, you might be asking about the part of the week that is not a weekend. As in "I do A during the week but on weekends I do B". "During the week" implying the regular workdays.
In this case, you can use "hét közben" for "during the week", and "hétvégén" for "on the weekend".
Mit csinálsz egy héten? = What do you do on a week?
"Mit csinálsz a héten?" can be changed into "Mit csinálsz ezen a héten?", & it still means "What are you doing this week?"
Note that the original sentence might refer to the next week if it's uttered on the weekend (I don't think you can do that in English, that's why I'm pointing it out.)