Based on audio recordings made once a month during the first 12 months of a child's life, we propose a new method for clustering this set of vocalizations. We use a topologically augmented representation of the vocalizations, employing two persistence diagrams for each vocalization: one computed on the surface of its spectrogram and one on the Takens' embeddings of the vocalization. A synthetic persistent variable is derived for each diagram and added to the MFCCs (Mel-frequency cepstral coefficients). Using this representation, we fit a non-parametric Bayesian mixture model with a Dirichlet process prior to model the number of components. This procedure leads to a novel data-driven categorization of vocal productions. Our findings reveal the presence of 8 clusters of vocalizations, allowing us to compare their temporal distribution and acoustic profiles in the first 12 months of life.