We consider whether a deep neural network trained with raw MEG data can be used to predict the age of children performing a verb-generation task, a monosyllable speech-elicitation task, and a multi-syllabic speech-elicitation task. Furthermore, we argue that the network makes predictions on the grounds of differences in speech development. Previous work has explored taking 'deep' neural networks (DNNs) designed for, or trained with, images to classify encephalographic recordings with some success, but this does little to acknowledge the structure of these data. Simple neural networks have been used extensively to classify data expressed as features, but require extensive feature engineering and pre-processing. We present novel DNNs trained using raw magnetoencephalography (MEG) and electroencephalography (EEG) recordings that mimic the feature-engineering pipeline. We highlight criteria the networks use, including relative weighting of channels and preferred spectro-temporal characteristics of re-weighted channels. Our data feature 92 subjects aged 4-18, recorded using a 151-channel MEG system. Our proposed model scores over 95% mean cross-validation accuracy distinguishing above and below 10 years of age in single trials of un-seen subjects, and can classify publicly available EEG with state-of-the-art accuracy.