We investigate the problem of reconfigurable intelligent surface (RIS)-aided monostatic sensing of a mobile target under line-of-sight (LoS) blockage considering a single antenna, full-duplex, and dual-functional radar-communications base station (BS). For the purpose of target detection and delay/Doppler/angle estimation, we derive a detector based on the generalized likelihood ratio test (GLRT), which entails a high-dimensional parameter search and leads to angle-Doppler coupling. To tackle these challenges, we propose a two-step algorithm for solving the GLRT detector/estimator in a low-complexity manner, accompanied by a RIS phase profile design tailored to circumvent the angle-Doppler coupling effect. Simulation results verify the effectiveness of the proposed algorithm, demonstrating its convergence to theoretical bounds and its superiority over state-of-the-art mobility-agnostic benchmarks.