Geographical mismatch between demand for care and availability of healthcare resources has been a major challenge during the COVID-19 pandemic. As such, inter-hospital patient transfers emerged as a key aspect of the pandemic response in many countries, including the US and Canada. We propose and study a class of transient queueing control problems to gain insights into the structure of “good” transfer policies. Specifically, we consider multiple parallel queues, starting with a large and possibly unbalanced initial condition, and seek discrete-time dynamic transfer policies that minimize the expected total cost over a finite-horizon or until the system reaches a desirable state. Costs are incurred as customers wait in queues, and are transferred between queues - including both variable and fixed transfer costs. We characterize the structure of the optimal policy for an associated discrete-time fluid control problem and investigate the robustness of the structure for the original stochastic problem. Using simulation experiments, we illustrate the performance of fluid-based policies and examine the value of optimal transfers. Finally, we discuss how the results can facilitate the search for an optimal transfer policy in a high-fidelity stochastic model of patient flow.