Existing barriers to efficient deep ultraviolet (UV) light-emitting diodes (LEDs) may be reduced or overcome by moving away from conventional planar growth and toward three-dimensional nanostructuring. Nanorods have the potential for enhanced doping, reduced dislocation densities, improved light extraction efficiency, and quantum wells free from the quantum-confined Stark effect. Here, we demonstrate a hybrid top-down/bottom-up approach to creating highly uniform AlGaN core-shell nanorods on sapphire repeatable on wafer scales. Our GaN-free design avoids self-absorption of the quantum well emission while preserving electrical functionality. The effective junctions formed by doping of both the n-type cores and p-type caps were studied using nanoprobing experiments, where we find low turn-on voltages, strongly rectifying behaviors and significant electron-beam-induced currents. Time-resolved cathodoluminescence measurements find short carrier liftetimes consistent with reduced polarization fields. Our results show nanostructuring to be a promising route to deep-UV-emitting LEDs, achievable using commercially compatible methods.