Prediction of combustion-related properties of (oxygenated) hydrocarbons is an important and challenging task for which quantitative structure-property relationship (QSPR) models are frequently employed. Recently, a machine learning method, graph neural networks (GNNs), has shown promising results for the prediction of structure-property relationships. GNNs utilize a graph representation of molecules, where atoms correspond to nodes and bonds to edges containing information about the molecular structure. More specifically, GNNs learn physicochemical properties as a function of the molecular graph in a supervised learning setup using a backpropagation algorithm. This end-to-end learning approach eliminates the need for selection of molecular descriptors or structural groups, as it learns optimal fingerprints through graph convolutions and maps the fingerprints to the physicochemical properties by deep learning. We develop GNN models for predicting three fuel ignition quality indicators, i.e., the derived cetane number (DCN), the research octane number (RON), and the motor octane number (MON), of oxygenated and nonoxygenated hydrocarbons. In light of limited experimental data in the order of hundreds, we propose a combination of multitask learning, transfer learning, and ensemble learning. The results show competitive performance of the proposed GNN approach compared to state-of-the-art QSPR models, making it a promising field for future research. The prediction tool is available via a web front-end at www.avt.rwth-aachen.de/gnn.