Landmark labeling in 3D head surfaces is an important and routine task in clinical practice to evaluate head shape, namely to analyze cranial deformities or growth evolution. However, manual labeling is still applied, being a tedious and time-consuming task, highly prone to intra-/inter-observer variability, and can mislead the diagnose. Thus, automatic methods for anthropometric landmark detection in 3D models have a high interest in clinical practice. In this paper, a novel framework is proposed to accurately detect landmarks in 3D infant's head surfaces. The proposed method is divided into two stages: (i) 2D representation of the 3D head surface; and (ii) landmark detection through a deep learning strategy. Moreover, a 3D data augmentation method to create shape models based on the expected head variability is proposed. The proposed framework was evaluated in synthetic and real datasets, achieving accurate detection results. Furthermore, the data augmentation strategy proved its added value, increasing the method's performance. Overall, the obtained results demonstrated the robustness of the proposed method and its potential to be used in clinical practice for head shape analysis.