National Statistical Organizations (NSOs) increasingly draw on Machine Learning (ML) to improve the timeliness and cost-effectiveness of their products. When introducing ML solutions, NSOs must ensure that high standards with respect to robustness, reproducibility, and accuracy are upheld as codified, e.g., in the Quality Framework for Statistical Algorithms (QF4SA; Yung et al. 2022). At the same time, a growing body of research focuses on fairness as a pre-condition of a safe deployment of ML to prevent disparate social impacts in practice. However, fairness has not yet been explicitly discussed as a quality aspect in the context of the application of ML at NSOs. We employ Yung et al. (2022)'s QF4SA quality framework and present a mapping of its quality dimensions to algorithmic fairness. We thereby extend the QF4SA framework in several ways: we argue for fairness as its own quality dimension, we investigate the interaction of fairness with other dimensions, and we explicitly address data, both on its own and its interaction with applied methodology. In parallel with empirical illustrations, we show how our mapping can contribute to methodology in the domains of official statistics, algorithmic fairness, and trustworthy machine learning.