We present a fully three-dimensional study of the multiexciton optical response of vertically coupled GaN-based quantum dots via a direct-diagonalization approach. The proposed analysis is crucial in understanding the fundamental properties of few-particle/exciton interactions and, more important, may play an essential role in the design/optimization of semiconductor-based quantum information processing schemes. In particular, we focus on the interdot exciton-exciton coupling, key ingredient in recently proposed all-optical quantum processors. Our analysis demonstrates that there is a large window of realistic parameters for which both biexcitonic shift and oscillator strength are compatible with such implementation schemes.