If I were to use "You needn't do shopping", I'd tag with "need you?" However, that construction is fairly uncommon these days in BrE. You are far more likely to hear "You don't need to do shopping, do you?"
Note that people do use "do shopping" but they use "go shopping" or the verb "shop" far more frequently.
You don't need to go shopping, do you?
You don't need to shop, do you?
Student or Learner