The static structure and the time-dependent self-diffusion motion of interacting Brownian particles in a model two-dimensional suspension are discussed. For the static structure we report Brownian dynamics results assuming a hard disk plus Yukawa pair potential. The self-diffusion properties of this model system are calculated from two independent theoretical approaches. In order to assess the accuracy of the predictions of these two theories, we also performed Brownian dynamics calculations of the time-dependent self-diffusion coefficient for a wide range of values of both the particle concentration and the pair potential coupling constant. We find that both theories reproduce very well the main features exhibited by the Brownian dynamics data. Quantitatively, there are some discrepancies between both theoretical predictions and the Brownian dynamics results, which are negligible at moderate couplings, but become larger for strongly coupled systems and long times.