We investigate the transport of dipolar indirect excitons along the growth plane of polar (Al, Ga) N/GaN quantum well structures by means of spatially and time-resolved photoluminescence spectroscopy. The transport in these strongly disordered quantum wells is activated by dipole-dipole repulsion. The latter induces an emission blue shift that increases linearly with exciton density, whereas the radiative recombination rate increases exponentially. Under continuous, localized excitation, we observe continuously decreasing emission energy, as excitons propagate away from the excitation spot. This corresponds to a steady-state gradient of exciton density, measured over several tens of micrometers. Time-resolved microphotoluminescence experiments provide information on the dynamics of recombination and transport of dipolar excitons. We account for the ensemble of experimental results by solving the nonlinear drift-diffusion equation. Quantitative analysis suggests that in such structures, exciton propagation on the scale of 10 to 20 mu m is mainly driven by diffusion, rather than by drift, due to the strong disorder and the presence of nonradiative defects. Secondary exciton creation, most probably by the intense higher-energy luminescence, guided along the sample plane, is shown to contribute to the exciton emission pattern on the scale up to 100 mu m. The exciton propagation length is strongly temperature dependent, the emission being quenched beyond a critical distance governed by nonradiative recombination.