Gait-based age estimation is a key technique for many applications. It is well known that age estimation uncertainty is highly dependent on age (i.e., small for children and large for adults), and it is important to know the uncertainty for the above-mentioned applications. Therefore, we propose a method for uncertainty-aware gait-based age estimation by introducing a label distribution learning framework. Specifically, we design a network that takes an appearance-based gait feature as input and outputs discrete label distributions in the integer age domain. We then train the network to minimize a loss function, which is defined as the dissimilarity between the estimated age distribution and the ground-truth age distribution, in addition to the conventional mean absolute error for the estimated age. Additionally, we demonstrate that uncertainty-aware gait-based age estimation is beneficial for two applications: person search by age query and people counting by age group. Experiments on the world's largest gait database, OULP-Age, demonstrated that the proposed method can successfully represent age estimation uncertainty, and outperforms or is comparable with state-of-the-art methods in terms of age estimation accuracy. Moreover, we demonstrated the effectiveness of the uncertainty-aware framework in applications to person search and people counting through experiments on the database.