The physics of iridium-based 5d transition metal oxides has attracted significant interest due to the potential for exotic magnetic and electronic ground states driven by strong spin-orbit coupling effects. Among the most extensively studied iridates is the layered perovskite Sr2IrO4, which was recently proposed as the first experimental realization of a novel Jeff=1/2 spin-orbital Mott insulating state. Intriguing similarities between Sr2IrO4 and La2CuO4, the parent compound of the high-Tc cuprates, have also led to speculation that it may be possible to induce superconductivity in this system through chemical doping. We have investigated the magnetic properties of the doped system Sr2Ir1-xRhxO4 using a combination of resonant magnetic x-ray scattering (RMXS), resonant inelastic x-ray scattering (RIXS), and x-ray absorption spectroscopy (XAS) techniques. These measurements reveal the effect of Rh-doping on the magnetic structure, phase diagram, and characteristic magnetic excitations of Sr2IrO4, and provide fundamental information about the role of quenched Rh impurities.