We discuss scanning near-field optical microscope based on original double resonant montage of a fibre probe onto the tuning fork and proprietary electronics capable of fast and precise measurements of the resonant frequency and the quality factor of sensor dithering. Special emphasis is given on the pulsed excitation/gated detection of optical signal. This option as well as the possibility of fast scanning facilitates a lot the problem of single fluorescence centres detection. To illustrate the performance of this microscope, we present first true single-molecule fluorescence resonance energy transfer scanning near-field optical microscope images of single CdSe nanocrystals on glass slide surface and observation of an optical 'pseudoresolution' of densely packed 100-nm-diameter transfluorescent spheres in noisy conditions.