This study investigates the complex interplay between the cardiac and respiratory systems in 268 healthy neonates born between 35 and 40 weeks of gestation. The aim is to provide a comprehensive description of the developing cardiorespiratory information transfer mechanisms as a function of gestational age (GA). This report proposes an extension of the traditional Transfer Entropy measure (TE), which employs multiple lagged versions of the time series of the intervals between two successive R waves of the QRS signal on the electrocardiogram (RR series) and respiration time series (RESP). The method aims to quantify the instantaneous and delayed effects between the two processes within a fine-grained time scale. Firstly, lagged TE was validated on a simulated dataset. Subsequently, lagged TE was employed on newborn cardiorespiratory data. Results indicate a progressive increase in information transfer as a function of gestational age, as well as significant differences in terms of instantaneous and delayed interactions between the cardiac and the respiratory system when comparing the two TE directionalities (RR→RESP vs. RESP→RR). The proposed investigation addresses the role of the different autonomic nervous system (ANS) branches involved in the cardiorespiratory system, since the sympathetic and parasympathetic branches operate at different time scales. Our results allow to infer that the two TE directionalities are uniquely and differently modulated by both branches of the ANS. TE adds an original quantitative tool to understanding cardiorespiratory imbalance in early infancy.