Manipulating the ferromagnetic interactions in diluted magnetic semiconductor quantum dots (DMSQDs) is a central theme to the development of next-generation spin-based information technologies, but this remains a great challenge because of the intrinsic antiferromagnetic coupling between impurity ions therein. Here, we propose an effective approach capable of activating ferromagnetic exchange in ZnO-based DMSQDs, by virtue of a core/shell structure that engineers the energy level of the magnetic impurity 3d levels relative to the band edge. This idea has been successfully applied to Zn0.96Co0.04O DMSQDs covered by a shell of ZnS or Ag2S. First-principles calculations further indicate that covering a ZnS shell around the Co-doped ZnO core drives a transition of antiferromagnetic-to-ferromagnetic interaction, which occurs within an effective depth of 1.2 nm underneath the surface in the core. This design opens up new possibility for effective manipulation of exchange interactions in doped oxide nanostructures for future spintronics applications.