Most infants are scanned during natural sleep to maximize successful data acquisition by minimizing head and body motion. However, our understanding of how different sleep states affect the infant's functional connectome remains to be determined. In this feasibility study, we develop a novel approach to quantify active and quiet sleep during fMRI using time-locked infant respiration in twenty infants scanned within 47 weeks postmenstrual age. Sleep state (active versus quiet sleep) was then coded using established validated procedures from respiratory variability. Based on this sleep state coding, we investigated differences in the functional connectome comparing active versus quiet sleep. Eleven infants had sufficient quality respiration data to identify sleep states. There were no significant differences in the functional connectome of infants during active and quiet sleep. Still, large effect sizes existed, suggesting that sleep effects may be important in some studies. These findings demonstrate the feasibility and practicality of acquiring respiration data during scanning to facilitate sleep state coding and further understand its relationship to the neurodevelopment of infants. Given the relative ease of collecting respiration data using this setup, we conservatively recommend a wider adoption of our approach.