This paper explores an innovative fusion of Quantum Computing (QC) and Artificial Intelligence (AI) through the development of a Hybrid Quantum Graph Convolutional Neural Network (HQGCNN), combining a Graph Convolutional Neural Network (GCNN) with a Quantum Multilayer Perceptron (MLP). The study highlights the potentialities of GCNNs in handling global-scale dependencies and proposes the HQGCNN for predicting complex phenomena such as the Oceanic Nino Index (ONI). Preliminary results suggest the model potential to surpass state-of-the-art (SOTA). The code will be made available with the paper publication.