if you're going to practice this drill, do it on a torso-sized target, forget the 3 inch bullseyes or whatever. your goal is to be able to put rounds into center mass while advancing towards it, away from it, or parallel to it.
your body does need to be able to fluidly move while shooting, because you might not be able to watch where you are stepping. having the knees slightly bent in a semi-crouch assists with this. as does leaning forward with your upper body, to help reduce muzzle flip.
"Every man alone is sincere; at the entrance of a second person hypocrisy begins." - Ralph Waldo Emerson
"People demand freedom of speech as a compensation for the freedom of thought which they seldom use." - Soren Kierkegaard