Resting-state functional connectivity is a widely used approach to study the functional brain network organization during early brain development. However, the estimation of functional connectivity networks in individual infants has been rather elusive due to the unique challenges involved with functional magnetic resonance imaging (fMRI) data from young populations. Here, we use fMRI data from the developing Human Connectome Project (dHCP) database to characterize individual variability in a large cohort of term-born infants (N = 289) using a novel data-driven Bayesian framework. To enhance alignment across individuals, the analysis was conducted exclusively on the cortical surface, employing surface-based registration guided by age-matched neonatal atlases. Using 10 minutes of resting-state fMRI data, we successfully estimated subject-level maps for eight brain networks along with individual functional parcellation maps that revealed differences between subjects. We also found a significant relationship between age and mean connectivity strength in all brain regions, including previously unreported findings in higher-order networks. These results illustrate the advantages of surface-based methods and Bayesian statistical approaches in uncovering individual variability within very young populations.