A metal nanoparticle coupled to a semiconductor quantum dot forms a tunable hybrid system which exhibits remarkable optical phenomena. Small metal nanoparticles possess nanocavitylike optical concentration capabilities due to the presence of strong dipolar excitation modes in the form of localized surface plasmons. Semiconductor quantum dots have strong luminescent capabilities widely used in many applications such as biosensing. When a quantum dot is kept in the vicinity of a metal nanoparticle, a dipole-dipole coupling occurs between the two nanoparticles giving rise to various optical signatures in the scattered spectra. This coupling makes the two nanoparticles behave like a single hybrid molecule. Hybrid molecules made of metal nanoparticles (MNPs) and quantum dots (QDs) under the influence of an external driving field have been extensively studied in literature, using the local response approximation (LRA). However, such previous work in this area was not adequate to explain some experimental observations such as the size-dependent resonance shift of metal nanoparticles which becomes quite significant with decreasing diameter. The nonlocal response of metallic nanostructures which is hitherto disregarded by such studies is a main reason for such nonclassical effects. The generalized nonlocal optical response (GNOR) model provides a computationally less-demanding path to incorporate such properties into the theoretical models. It allows unified theoretical explanation of observed experimental phenomena which previously seemed to require ab initio microscopic theory. In this paper, we analyze the hybrid molecule in an external driving field as an open quantum system using a cavity-QED approach. In the process, we quantum mechanically model the dipole moment operator and the dipole response field of the metal nanoparticle taking the nonlocal effects into account. We observe that the spectra resulting from the GNOR based model effectively demonstrate the experimentally observed size dependent amplitude scaling, linewidth broadening, and resonance shift phenomena compared to the respective LRA counterparts. Then, we provide a comparison between our suggested GNOR based cavity-QED model and the conventional LRA model, where it becomes evident that our analytical model provides a close match to the experimentally suggested behavior. Furthermore, we show that the Rayleigh scattering spectra of the MNP-QD hybrid molecule possess an asymmetric Fano interference pattern that is tunable to suit various applications.