Human auditory perception is shaped by moving sound sources in 3D space, yet prior work in generative sound modelling has largely been restricted to mono signals or static spatial audio. In this work, we introduce a framework for generating moving sounds given text prompts in a controllable fashion. To enable training, we construct a synthetic dataset that records moving sounds in binaural format, their spatial trajectories, and text captions about the sound event and spatial motion. Using this dataset, we train a text-to-trajectory prediction model that outputs the three-dimensional trajectory of a moving sound source given text prompts. To generate spatial audio, we first fine-tune a pre-trained text-to-audio generative model to output temporally aligned mono sound with the trajectory. The spatial audio is then simulated using the predicted temporally-aligned trajectory. Experimental evaluation demonstrates reasonable spatial understanding of the text-to-trajectory model. This approach could be easily integrated into existing text-to-audio generative workflow and extended to moving sound generation in other spatial audio formats.