Background/Objectives: Endogenous oscillations reflect the spontaneous activity of brain networks involved in cognitive processes. In adults, endogenous activity across different bands correlates with, and can even predict, language and speech perception processing. However, it remains unclear how this activity develops in children with typical and atypical development. Methods: We investigated differences in resting-state EEG between preschoolers with developmental language disorder (DLD), their age-matched controls with typical language development (TLD), and a group of adults. Results: We observed significantly lower oscillatory power in adults than in children (p < 0.001 for all frequency bands), but no differences between the groups of children in power or hemispheric lateralisation, suggesting that oscillatory activity reflects differences in age, but not in language development. The only measure that differed between the children's groups was theta/alpha band ratio (p = 0.004), which was significantly smaller in TLD than in DLD children, although this was an incidental finding. Behavioural results also did not fully align with previous research, as TLD children performed better in the filtered speech test (p = 0.01), but not in the speech-in-babble one, and behavioural test scores did not correlate with high-frequency oscillations, lateralisation indices, or band ratio measures. Conclusions: We discuss the suitability of these resting-state EEG measures to capture group-level differences between TLD/DLD preschoolers and the relevance of our findings for future studies investigating neural markers of typical and atypical language development.