The widespread success of the WLAN technology raises the need for the efficient management of the different access points and the associated wireless devices, especially when multimedia and other QoS demanding applications are employed. In this paper we propose an autonomic load balancing mechanism for WLAN networks and test its applicability for a Voice over WLAN (VoWLAN) use case. The algorithm takes into account the channel utilization, the spatial distribution of wireless devices and the QoS requirements of user applications. The autonomic aspect of our algorithm is related to the use of a knowledge plane, which is a conceptual authority that entertains detailed runtime knowledge about the network state in terms of the load on each access point, as well as the connection speed and application QoS requirements of each wireless device. We use OPNET to evaluate the effectiveness of our management solution and load balancing algorithm. The paper presents the conducted simulations and ends by a critique of the general applicability of our algorithm and suggestions for future work.