The domain of image classification has been seen to be dominated by high-performing deep-learning (DL) architectures. However, the success of this field, as seen over the past decade, has resulted in the complexity of modern methodologies scaling exponentially, commonly requiring millions of parameters. Quantum computing (QC) is an active area of research aimed toward greatly reducing problems of complexity faced in classical computing. With growing interest toward quantum machine learning (QML) for applications of image classification, many proposed algorithms require usage of numerous qubits. In the noisy intermediate-scale quantum (NISQ) era, these circuits may not always be feasible to execute effectively; therefore, we should aim to use each qubit as effectively and efficiently as possible, before adding additional qubits. This article proposes a new single-qubit-based deep quantum neural network for image classification that mimics traditional convolutional neural network (CNN) techniques, resulting in a reduced number of parameters compared with previous works. Our aim is to prove the concept of the initial proposal by demonstrating classification performance of the single-qubit-based architecture, as well as to provide a tested foundation for further development. To demonstrate this, our experiments were conducted using various datasets including MNIST, Fashion-MNIST, and ORL face datasets. To further our proposal in the context of the NISQ era, our experiments were intentionally conducted in noisy simulation environments. Initial test results appear promising, with classification accuracies of 94.6%, 89.5%, and 82.5% achieved on the subsets of MNIST, FMNIST, and ORL face datasets, respectively. In addition, proposals for further investigation and development were considered, where it is hoped that these initial results can be improved.