Congenital Heart Disease (CHD) is a group of cardiac malformations present already during fetal life, representing the prevailing category of birth defects globally. Our aim in this study is to aid 3D fetal vessel topology visualisation in aortic arch anomalies, a group which encompasses a range of conditions with significant anatomical heterogeneity. We present a multi-task framework for automated multi-class fetal vessel segmentation from 3D black blood T2w MRI and anomaly classification. Our training data consists of binary manual segmentation masks of the cardiac vessels' region in individual subjects and fully-labelled anomaly-specific population atlases. Our framework combines deep learning label propagation using VoxelMorph with 3D Attention U-Net segmentation and DenseNet121 anomaly classification. We target 11 cardiac vessels and three distinct aortic arch anomalies, including double aortic arch, right aortic arch, and suspected coarctation of the aorta. We incorporate an anomaly classifier into our segmentation pipeline, delivering a multi-task framework with the primary motivation of correcting topological inaccuracies of the segmentation. The hypothesis is that the multi-task approach will encourage the segmenter network to learn anomaly-specific features. As a secondary motivation, an automated diagnosis tool may have the potential to enhance diagnostic confidence in a decision support setting. Our results showcase that our proposed training strategy significantly outperforms label propagation and a network trained exclusively on propagated labels. Our classifier outperforms a classifier trained exclusively on T2w volume images, with an average balanced accuracy of 0.99 (0.01) after joint training. Adding a classifier improves the anatomical and topological accuracy of all correctly classified double aortic arch subjects.