Wurtzite GaN/AlN quantum dots (QDs) are studied by time-resolved photoluminescence. Careful measurements allow us to reach the regime of a single electron-hole pair per dot, evidenced by a monoexponential decay of the luminescence and a stop of the time-dependent shift of the emission energy. The transition energy and the radiative lifetime of the QD ground state are measured in the absence of any electric field screening effect, for a wide range of QD heights. These results are analyzed within an envelope function model for the electron and hole confinement. The effective electric field, averaged over the strain distribution in the dots, is determined to be of 9.0 +/- 0.5 MV/cm.