In recent years, semiconductor nanodots have been actively used for biolabeling. We propose using alternate composite nanostructures consisting of a semiconductor size-quantized core covered by a nanometer-thick Au shell, having two principal advantages over purely semiconducting nanodots: (i) reduction of toxicity due to a complete Au coverage of the cores containing potentially poisonous Cd, Se, or Pb; (ii) amplification of exciting and/or emitted light by plasmon effects in a metallic shell which will increase the imaging efficiency. Theoretical calculations show that the optical absorption and emission spectra have several peaks corresponding to interband transitions in the core, and the two plasmon modes in the Au shell. When the energy of interband transitions coincides with one of the plasmon peaks, the resonant electromagnetic field in the core is enhanced which should result in amplification of the luminescence intensity. Especially effective amplification can be reached if the frequencies of the exciting and emitting light both match two plasmon peaks. Experimental measurements were performed with composite nanostructures containing CdSe-ZnS cores fabricated by the organo-metallic method, followed by deposition of the gold shell using thermal decomposition of a Au (I) precursor. These revealed a multimodal structure of the absorption and luminescence spectra, good tunability, high intensity, and narrow emission linewidth. The dependence of spectra on the thickness of Au shell was investigated. The measurements were performed in different biological media and demonstrated stability and environment-insensitivity - a prerequisite for biolabeling.