In this paper, we consider a problem motivated by search-and-rescue applications, where an unmanned aerial vehicle (UAV) seeks to approach the vicinity of a distant quasi-stationary radio frequency (RF) emitter surrounded by local scatterers. The UAV employs only measurements of the Doppler frequency of the received RF signal, along with its own bearing, to continuously adapt its trajectory. We propose and evaluate a trajectory planning approach that addresses technical difficulties such as the unknown carrier frequency offset between the emitter and the UAV's receiver, the frequency drifts of the local oscillators over time, the direction ambiguity in Doppler, and the noise in the observations. For the initial trajectory, the UAV estimates the direction of the emitter using a circular motion, which resolves direction ambiguity. The trajectory is then continuously adapted using feedback from frequency measurements obtained by perturbing the bearing around the current trajectory. We show that the proposed algorithm converges to the vicinity of the emitter, and illustrate its efficacy using simulations.