The neural processes underpinning cognition and language development in infancy are of great interest. We investigated EEG power and coherence in infancy, as a reflection of underlying cortical function of single brain region and cross-region connectivity, and their relations to cognition and language development. EEG recordings were longitudinally collected from 21 infants with typical development between 1 and 7 months. We investigated relative band power at theta (3-6Hz) and alpha (6-9Hz) and EEG coherence of these frequency bands at 25 electrode pairs that cover key brain regions. A correlation analysis was performed to assess the relationship between EEG measurements (frequency bands and brain regions) and raw Bayley cognitive and language developmental scores. In the first months of life, relative band power is not correlated with changes in cognitive and language scales. However, theta coherence is negatively correlated with receptive language scores between frontoparietal regions, and alpha coherence is negatively correlated with expressive language scores between frontoparietal regions. The results from this preliminary study are the first steps in identifying potential biomarkers of early cognitive and language development. In future work, we will confirm norm references of early cognitive and language development that can be compared with infants at risk for neurodevelopmental disabilities.