Quantum plasmonics of few electrons that was reported a few years ago in photodoping experiments has received little or no attention in doped nanomaterials both theoretically and experimentally. In this work, we studied extensively the absorption spectra of a protype quantum dot of sizeable ZnO of approximately 3.0 nm in diameter doped with Ga, and Al in lightly diluted limit with density functional theory (DFT) plus Hubbard corrections (U). We found uniform distribution of dopants on facets around outermost surface results in spectral lines with narrower line widths. Our results also show classification of transitions into intraband and interband is not applicable to discrete energy spectra of low-lying states above the LUMO. For a wurtzite quantum dot of ZnO, only polarization along the c axis results in collective electron transitions in contrast to the polarization along the a axis. Ga is a better dopant than Al, with narrower spectral line widths because of the localized 3d electrons screening off Coulomb interactions. As expected, comparison of the 3.0 nm results to 2.0 nm shows much more broadened spectral lines for the 2.0 nm QD. Our work shows that the DFT + U method with numerical atomic basis can be used at reasonable computational cost to study quantum plasmonics. The method can be extended to study magneto-optics of diluted magnetic semiconductor QDs.