Hybrid materials formed by semiconductor quantum dots and J-aggregates of cyanine dyes provide a unique combination of enhanced absorption in inorganic constituents with large oscillator strength and extremely narrow exciton bands of the organic component. The optical properties of dendrite structures with fractal dimension 1.7-1.8, formed from J-aggregates integrated with CdTe quantum dots (QDs), have been investigated by photoluminescence spectroscopy and fluorescence lifetime imaging microscopy. Our results demonstrate that (i) J-aggregates are coupled to QDs by Förster-type resonant energy transfer and (ii) there are energy fluxes from the periphery to the centre of the structure, where the QD density is higher than in the periphery of the dendrite. Such an anisotropic energy transport can be only observed when dendrites are formed from QDs integrated with J-aggregates. These QD/J-aggregate hybrid systems can have applications in light harvesting systems and optical sensors with extended absorption spectra.