This paper presents a new dual quaternion-based formulation for pose-based visual servoing. Extending our previous work on local contact moment (LoCoMo) based grasp planning, we demonstrate grasping of arbitrarily moving objects in 3D space. Instead of using the conventional axis-angle parameterization, dual quaternions allow designing the visual servoing task in a more compact manner and provide robustness to manipulator singularities. Given an object point cloud, LoCoMo generates a ranked list of grasp and pre-grasp poses, which are used as desired poses for visual servoing. Whenever the object moves (tracked by visual marker tracking), the desired pose updates automatically. For this, capitalising on the dual quaternion spatial distance error, we propose a dynamic grasp re-ranking metric to select the best feasible grasp for the moving object. This allows the robot to readily track and grasp arbitrarily moving objects. In addition, we also explore the robot null-space with our controller to avoid joint limits so as to achieve smooth trajectories while following moving objects. We evaluate the performance of the proposed visual servoing by conducting simulation experiments of grasping various objects using a 7-axis robot fitted with a 2-finger gripper. Obtained results demonstrate the efficiency of our proposed visual servoing.