A total dominator coloring of a graph G is a proper coloring of G in which each vertex of the graph is adjacent to all vertices of a color class. The minimum number of color classes in a total dominator coloring of a graph is called its total dominator chromatic number. Here, we study the total domination and total dominator chromatic numbers of Moore graphs which are a family of k-regular graph of girth g and have the smallest order n0(k,g) (a known number in terms of k and g).