Fetal health monitoring through one-dimensional Doppler ultrasound (DUS) signals offers a cost-effective and accessible approach that is increasingly gaining interest. Despite its potential, the development of machine learning based techniques to assess the health condition of mothers and fetuses using DUS signals remains limited. This scarcity is primarily due to the lack of extensive DUS datasets with a reliable reference for interpretation and data imbalance across different gestational ages. In response, we introduce a novel autoregressive generative model designed to map fetal electrocardiogram (FECG) signals to corresponding DUS waveforms (Auto-FEDUS). By leveraging a neural temporal network based on dilated causal convolutions that operate directly on the waveform level, the model effectively captures both short and long-range dependencies within the signals, preserving the integrity of generated data. Cross-subject experiments demonstrate that Auto-FEDUS outperforms conventional generative architectures across both time and frequency domain evaluations, producing DUS signals that closely resemble the morphology of their real counterparts. The realism of these synthesized signals was further gauged using a quality assessment model, which classified all as good quality, and a heart rate estimation model, which produced comparable results for generated and real data, with a Bland-Altman limit of 4.5 beats per minute. This advancement offers a promising solution for mitigating limited data availability and enhancing the training of DUS-based fetal models, making them more effective and generalizable.