Context Baleen whale calves rapidly increase in size and improve locomotion abilities, while on their low-latitude breeding ground, allowing them to undertake a successful migration to high-latitude feeding grounds. Aims We investigated energy expenditure and resting behaviour of humpback whale (Megaptera novaeangliae) mother–calf pairs in regard to changes in calf length on an undisturbed breeding/resting ground off Exmouth Gulf, Western Australia. Methods Data were collected from August to October in 2018 and 2019 on lactating mothers that were predominantly resting on the surface with their calf. Focal follows on mother–calf pairs (n = 101) were conducted using an unmanned aerial vehicle to obtain detailed video of behaviours and respirations (23.7 h). Body length measurements of individual whales were calculated from aerial still frames. Key results Results on calves ranging in length from ~4–8 m demonstrated that calf respiration rate decreased with an increase in calf length and increased with presence of activity (P < 0.001). Calf inter-breath intervals became longer in duration with an increase in calf length (P < 0.01). Calf activity level and resting behaviour remained constant, with calves logging for 53% of the time their mothers were logging. Maternal respiration rate remained low and did not differ with respect to maternal or calf length. Conclusions Results highlighted the importance of resting grounds for energy preservation, which benefits the calves’ rapid growth before migration to polar waters. Implications Findings from the present largely undisturbed population serve as a baseline for understanding the impacts of anthropogenic disturbance on resting behaviour and energy expenditure in humpback whale mother–calf pairs globally.