In this work, we aim to investigate whether information based metrics of neural activity are a useful tool for the quantification of consciousness before and shortly after birth. Neural activity is measured using fetal magnetoencephalography (fMEG) in human fetuses and neonates. Based on recent theories on consciousness, information-based metrics are established to measure brain complexity and to assess different levels of consciousness. Different metrics (measures of entropy, compressibility and fractality) are, thus, explored in a reference population and their usability is evaluated. For comparative analysis, two fMEG channels were selected: one where brain activity was previously detected and one at least 15 cm away, that represented a control channel. The usability of each metric was evaluated and results from the brain and control channel were compared. Concerning the ease of use with fMEG data, Lempel-Ziv-Complexity (LZC) was evaluated as best, as it is unequivocal and needs low computational effort. The fractality measures have a high number of parameters that need to be adjusted prior to analysis and therefore forfeit comparability, while entropy measures require a higher computational effort and more parameters to adjust compared to LZC. Comparison of a channel with brain activity and a control channel in neonatal recordings showed significant differences in most complexity metrics. This clear difference can be seen as proof of concept for the usability of complexity metrics in fMEG. For fetal data, this comparison produced less clear results which can be related to leftover maternal signals included in the control channel. Further work is necessary to conclusively interpret results from the analysis of fetal recordings. Yet this study shows that complexity metrics can be used for fMEG data on early consciousness and the evaluation gives a guidance for future work. The inconsistency of results from different metrics highlights the challenges of working with complexity metrics as neural correlates of consciousness, as well as the caution one should apply to interpret them.