Due to the characteristics of COVID-19, the epidemic develops rapidly and overwhelms health service systems worldwide. Many patients suffer from systemic life-threatening problems and need to be carefully monitored in ICUs. Thus the intelligent prognosis is in an urgent need to assist physicians to take an early intervention, prevent the adverse outcome, and optimize the medical resource allocation. However, in the early stage of the epidemic outbreak, the data available for analysis is limited due to the lack of effective diagnostic mechanisms, rarity of the cases, and privacy concerns. In this paper, we propose a deep-learning-based approach, CovidCare, which leverages the existing electronic medical records to enhance the prognosis for inpatients with emerging infectious diseases. It learns to embed the COVID-19-related medical features based on massive existing EMR data via transfer learning. The transferred parameters are further trained to imitate the teacher model's representation behavior based on knowledge distillation, which embeds the health status more comprehensively in the source dataset. We conduct the length of stay prediction experiments for patients on a real-world COVID-19 dataset. The experiment results indicate that our proposed model consistently outperforms the comparative baseline methods. CovidCare also reveals that, 1) hs-cTnI, hs-CRP and Platelet Counts are the most fatal biomarkers, whose abnormal values usually indicate emergency adverse outcome. 2) Normal values of gamma-GT, AP and eGFR indicate the overall improvement of health. The medical findings extracted by CovidCare are empirically confirmed by human experts and medical literatures.