The effects of edge hydrogenation and hydroxylation on the relative stability and electronic properties of hexagonal boron nitride quantum dots (h-BNQDs) are investigated. Zigzag edge hydroxylation is found to result in considerable energetic stabilization of h-BNQDs as well as a reduction of their electronic gap with respect to their hydrogenated counterparts. The application of an external in-plane electric field leads to a monotonous decrease of the gap. When compared to their edge-hydrogenated counterparts, significantly lower field intensities are required to achieve full gap closure of the zigzag edge hydroxylated h-BNQDs. These results indicate that edge chemistry may provide a viable route for the design of stable and robust electronic devices based on nanoscale hexagonal boron-nitride systems.