Normal fetal adipose tissue (AT) development is essential for perinatal well-being. AT, or simply fat, stores energy in the form of lipids. Malnourishment may result in excessive or depleted adiposity. Although previous studies showed a correlation between the amount of AT and perinatal outcome, prenatal assessment of AT is limited by lacking quantitative methods. Using magnetic resonance imaging (MRI), 3D fat- and water-only images of the entire fetus can be obtained from two point Dixon images to enable AT lipid quantification. This paper is the first to present a methodology for developing a deep learning based method for fetal fat segmentation based on Dixon MRI. It optimizes radiologists' manual fetal fat delineation time to produce annotated training dataset. It consists of two steps: 1) model-based semi-automatic fetal fat segmentations, reviewed and corrected by a radiologist; 2) automatic fetal fat segmentation using DL networks trained on the resulting annotated dataset. Three DL networks were trained. We show a significant improvement in segmentation times (3:38 hours to < 1 hour) and observer variability (Dice of 0.738 to 0.906) compared to manual segmentation. Automatic segmentation of 24 test cases with the 3D Residual U-Net, nn-UNet and SWIN-UNetR transformer networks yields a mean Dice score of 0.863, 0.787 and 0.856, respectively. These results are better than the manual observer variability, and comparable to automatic adult and pediatric fat segmentation. A radiologist reviewed and corrected six new independent cases segmented using the best performing network, resulting in a Dice score of 0.961 and a significantly reduced correction time of 15:20 minutes. Using these novel segmentation methods and short MRI acquisition time, whole body subcutaneous lipids can be quantified for individual fetuses in the clinic and large-cohort research.