We have performed Monte-Carlo simulations of the charge carrier transport in a model molecularly doped polymer using three most popular hopping theories (the dipolar glass model, the Gaussian disorder model, and an intermediate between them) in a wide range of applied electric fields and temperatures. Time of flight transients have been computed and analyzed in logarithmic coordinates to study the Poole-Frenkel field dependence, the non-Arrhenius mobility temperature dependence, and the nondispersive versus dispersive current shapes. We also have made an attempt to estimate the total disorder energy directly from simulation data at the lowest electric field thus checking the consistency of the model fitting. Computational results have been compared with the analytical and experimental information available in the literature.