The use of artificial intelligence (AI) in automated disease classification significantly reduces healthcare costs and improves the accessibility of services. However, this transformation has given rise to concerns about the fairness of AI, which disproportionately affects certain groups, particularly patients from underprivileged populations. Recently, a number of methods and large-scale datasets have been proposed to address group performance disparities. Although these methods have shown effectiveness in disease classification tasks, they may fall short in ensuring fair prediction of disease progression, mainly because of limited longitudinal data with diverse demographics available for training a robust and equitable prediction model. In this paper, we introduce TransFair to enhance demographic fairness in progression prediction for ocular diseases. TransFair aims to transfer a fairness-enhanced disease classification model to the task of progression prediction with fairness preserved. Specifically, we train a fair EfficientNet, termed FairEN, equipped with a fairness-aware attention mechanism using extensive data for ocular disease classification. Subsequently, this fair classification model is adapted to a fair progression prediction model through knowledge distillation, which aims to minimize the latent feature distances between the classification and progression prediction models. We evaluate FairEN and TransFair for fairness-enhanced ocular disease classification and progression prediction using both two-dimensional (2D) and 3D retinal images. Extensive experiments and comparisons with models with and without considering fairness learning show that TransFair effectively enhances demographic equity in predicting ocular disease progression.