This paper presents a learning system that uses Q-learning with a resource allocating network (RAN) for behavior learning in mobile robotics. The RAN is used as a function approximator, and Q-learning is used to learn the control policy in `off-policy' fashion that enables learning to be bootstrapped by a prior knowledge controller, thus speeding up the reinforcement learning. Our approach is verified on a PeopleBot robot executing a visual servoing based docking behavior in which the robot is required to reach a goal pose. Further experiments show that the RAN network can also be used for supervised learning prior to reinforcement learning in a layered architecture, thus further improving the performance of the docking behavior.