"What are you doing" is a 'continuous' form... it means what is it that you will do throughout this week. There is an old romantic American song; "What are you doing for the rest of your life?"
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You could say "what do you do this week" but it would have an entirely different meaning. Consider this conversation:
"Last week I speed skated from Moscow to St Petersburg!"
"Really? What do you do this week, then? Run to Berlin?""
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Compare this use of do:
"Do you play tennis?"
"No I do not play tennis. I do not have the money or the time to play tennis."
"Do try to find the time. I think you will be good at tennis and I do want to help you to find a teacher if you have the time."