We study theoretically the quantum optical properties of hybrid molecules composed of an individual quantum dot and a metallic nanoparticle. We calculate the resonance fluorescence of this composite system. Its incoherent part, arising from nonlinear quantum processes, is enhanced by more than 2 orders of magnitude as compared to that of the dot alone. The coupling between the two systems gives rise to a Fano interference effect which strongly influences the quantum statistical properties of the scattered photons: a small frequency shift of the incident light field may cause changes in the intensity correlation function of the scattered field of orders of magnitude. The system opens a good perspective for applications in active metamaterials and ultracompact single-photon devices.