We have investigated the problem of learning an effective model for molecular property prediction on small-sample datasets typically encountered in the final stages of screening cascades characteristic of molecular design and drug discovery. Our focus was on showing the utility of transfer learning with graph neural networks for the multi-fidelity nature of this generative data process. More specifically, we have mainly focused on knowledge transfer between large-scale low-fidelity measurements that are inexpensive to obtain and sparse high-fidelity observations that are labour and resource intensive. Typically, the effectiveness of the whole discovery process hinges on the assumption that one will be able to successfully select candidates for the final high-fidelity screening step. While prior work in materials chemistry has studied aspects of learning in multi-fidelity settings , our work is the first, to the best of our knowledge, that tackles novel and heterogeneous drug discovery by HTS tasks and quantum mechanics simulations through transfer learning with GNNs. We demonstrated a high level of generality through the successful application to quantum chemistry where we outperform existing methods, through explicitly evaluating transductive and inductive cases, through consistently strong results not only for our supervised VGAE architecture but also for 3D-aware networks like SchNet, and through extensions to more than two fidelities.