We propose an automated framework for predicting age and neurodevelopmental maturation of a fetus based on 3D ultrasound (US) brain image appearance. A topology-preserving manifold representation of the fetal skull enabled design of bespoke scale-invariant image features. Our regression forest model used these features to learn a mapping from age-related sonographic image patterns to fetal age and development. The Sylvian Fissure was identified as a critical region for accurate age estimation, and restricting the search space to this anatomy improved prediction accuracy on a set of 130 healthy fetuses (error ± 3.8 days; r = 0.98 performing the best current clinical method. Our framework remained robust when applied to a routine clinical population.