Health is certainly a valuable asset in the life of every human being and of particular relevance for a flourishing childhood. As empirical research concerning the social determinants of health shows, its distribution can, at least to a certain extent, be influenced by the way a society is arranged. Many philosophers now acknowledge that a fair distribution of health has to be a central part of a just society and they discuss to what extent a right to health can be justified. However, they do not typically distinguish between physical and mental health and neglect the special problems arising from these distinct, though related, perspectives. In this paper, we argue in favour of such a distinction and ask whether a minimally just society ought to include mental health among the goods that are to be distributed in a fair way among its children. Furthermore, we investigate the relationship between mental health and happiness and ask whether making mental health a subject of justice implies that children are entitled not only to a healthy but also to a happy childhood. Despite the positive impact of happiness on the lives of children, we conclude that happiness cannot be incorporated into a functional theory of justice, since it does not fully meet the criteria of objectivity, measurability and influenceability.