A direct single-step catalyst-free CVD technique has been used for producing alumina nano-whiskers covered by a few layers of defective graphene. The hybrid whiskers have been then exploited as electroconductive fillers to oxide ceramics. The electrically conductive additives do not substantially change the mechanical properties. However, the resistivity of the composites undergoes a considerable drop turning the dielectric oxides into conductive composites by addition of 2 vol% of fillers. Three-dimensional Monte Carlo simulation of systems of polydisperse prolate ellipsoids, using the critical path based tunneling-percolation model, has been exploiting for estimation of a tunnelling length-scale. The value of percolation threshold is found to be 2.23 nm for the materials under consideration, with is in a good agreement with experimental data.