Image classification is an important application for deep learning. With the advent of quantum technology, quantum neural networks (QNNs) have become the focus of research. Traditional deep learning-based image classification involves using a convolutional neural network (CNN) to extract features from the image and a multi-layer perceptron (MLP) network to create the decision boundaries. However, quantum circuits with parameters can extract rich features from images and also create complex decision boundaries. This paper proposes a hybrid QNN (H-QNN) model designed for binary image classification that capitalizes on the strengths of quantum computing and classical neural networks. Our H-QNN model uses a compact, two-qubit quantum circuit integrated with a classical convolutional architecture, making it highly efficient for computation on noisy intermediate-scale quantum (NISQ) devices that are currently leading the way in practical quantum computing applications. Our H-QNN model significantly enhances classification accuracy, achieving a 90.1% accuracy rate on binary image datasets. In addition, we have extensively evaluated baseline CNN and our proposed H-QNN models for image retrieval tasks. The obtained quantitative results exhibit the generalization of our H-QNN for downstream image retrieval tasks. Furthermore, our model addresses the issue of overfitting for small datasets, making it a valuable tool for practical applications.