Fetal head circumference (HC) is a key biometric indicator in prenatal ultrasound, essential for gestational age estimation and fetal growth assessment. However, conventional Convolutional Neural Networks (CNN)-based segmentation models often struggle to capture long-range dependencies, which hinders segmentation accuracy. To address this, we introduce Swin-DAG-VNet, a hybrid segmentation model which builds upon the Deeply Supervised Attention-Gated V-Net (DAG V-Net) as the baseline and integrates Swin Transformer to enhance global context modeling while preserving fine-grained structural details. Additionally, we incorporate Swin-Net-Add, a Transformer-enhanced feature fusion module, to improve multi-scale feature aggregation and boundary delineation. Furthermore, we employ an elliptical parameter regression method to predict key biometric parameters from the segmented contour, combines with an adaptive contour sampling strategy to refine segmentation, reducing noise and improving robustness. A physical calibration module ensures accurate real-world HC measurements. Experiments on the HC18 dataset demonstrate that Swin-DAG-VNet achieves an absolute difference (AD) of 1.78 mm, reducing absolute measurement bias by 5.3% compared to DAG V-Net, setting a new benchmark in the estimation of fetal HC.