Critically ill children who require inter-hospital transfers to paediatric intensive care units are sicker than other admissions and have higher mortality rates. Current transport practice primarily relies on early clinical assessments within the initial hours of transport. Real-time mortality risk during transport is lacking due to the absence of data-driven assessment tools. Addressing this gap, our research introduces the PROMPT (Patient-centred Real-time Outcome monitoring and Mortality PredicTion), an explainable end-to-end machine learning pipeline to forecast 30-day mortality risks. The PROMPT integrates continuous time-series vital signs and medical records with episode-specific transport data to provide real-time mortality prediction. The results demonstrated that with PROMPT, both the random forest and logistic regression models achieved the best performance with AUROC 0.83 (95% CI: 0.79-0.86) and 0.81 (95% CI: 0.76-0.85), respectively. The proposed model has demonstrated proof-of-principle in predicting mortality risk in transported children and providing individual-level model interpretability during inter-hospital transports.