We present quasi-particle (QP) corrections to the electronic energies for small GaP fullerenes, a new class of nanoscaled materials predicted to be stable and to show spontaneous formation. Using Time-Dependent Density Functional Theory we also computed the optical absorption spectra. The comparison between single-particle and optical absorption spectra yields strong excitonic effects with bonding energy up to 3.5 eV. The QP corrected HOMO-LUMO energy gaps confirm the high stability predicted for such molecules using ground-state computational schemes. The present results can be useful to identify the successful synthesis of these systems via optical absorption and QP spectra.