Coupling a single quantum emitter, such as a fluorescent molecule or a quantum dot (QD), to a plasmonic nanostructure is an important issue in nano-optics and nano-spectroscopy, relevant for a wide range of applications, including tip-enhanced near-field optical microscopy, plasmon enhanced molecular sensing and spectroscopy, and nanophotonic amplifiers or nanolasers, to mention only a few. While the field enhancement of a sharp nanoantenna increasing the excitation rate of a very closely positioned single molecule or QD has been well investigated, the detailed physical mechanisms involved in the emission of a photon from such a system are, by far, less investigated. In one of our ongoing research projects, we try to address these issues by constructing and spectroscopically analysing geometrically simple hybrid heterostructures consisting of sharp gold cones with single quantum dots attached to the very tip apex. An important goal of this work is to tune the longitudinal plasmon resonance by adjusting the cones' geometry to the emission maximum of the core-shell CdSe/ZnS QDs at nominally 650 nm. Luminescence spectra of the bare cones, pure QDs and hybrid systems were distinguished successfully. In the next steps we will further investigate, experimentally and theoretically, the optical properties of the coupled systems in more detail, such as the fluorescence spectra, blinking statistics, and the current results on the fluorescence lifetimes, and compare them with uncoupled QDs to obtain a clearer picture of the radiative and non-radiative processes.