Functional brain development in early infancy is a highly dynamic and complex process. Understanding each brain region’s topological role and its development in the brain functional connectivity (FC) networks is essential for early disorder detection. A handful of previous studies have mostly focused on how FC network is changing regarding age. These approaches inevitably overlook the effect of individual variability for those at the same age that could shape unique cognitive capabilities and personalities among infants. With that in mind, we propose a novel computational framework based on across-subject across-age multilayer network analysis with a fully automatic (for parameter optimization), robust community detection algorithm. By detecting group consistent modules without losing individual information, this method allows a first-ever dissociation analysis of the two variability sources – age dependency and individual specificity – that greatly shape early brain development. This method is applied to a large cohort of 0–2 years old infants’ functional MRI data during natural sleep. We not only detected the brain regions with greatest flexibility in this early developmental period but also identified five categories of brain regions with distinct development-related and individually variable flexibility changes. Our method is highly valuable for more thorough understanding of the early brain functional organizations and sheds light on early developmental abnormality detection.