Both question and answer seem fine to me but I'd ask "What are you going to do right now"? and answer "I'm going to the pub"

What will you do right now is very serious, something they say in action movies.

Depends on what you are trying to ask. "What will you do right now?" Will means a decision to be made at the moment of speaking.

It should be "What are you doing right now?" The answer should be "I am at the mall." Because the words "right now" mean at this moment, so use present continuous tense. If your friend wants to know what you will do later in the day, you can't use "right now". Use future tense: What will you do later today? I will go to the mall.