Why was Gimli of such a low rank, compared to the other representatives chosen for the Fellowship?

Part of the members of the Fellowship were chosen as representatives of their race: Legolas for the Elves, Boromir for mankind and Gimli for the dwarves. Of those three, two were the heirs of a ruler at the time (king Thranduil and the steward Denethor, who was de-facto king). Gimli, however, is simply the "son of Gloin", who, while surely significant, is of much lesser rank than the other two. According to this family tree, Gimli's most common ancestor with Dain II Ironfoot, the ruler of his house at the time, was four to five generations in the past.

My question is: Why was Gimli, as the representatives of the dwarves, of such a low rank, compared to the other representatives? Furthermore, is this fact of larger significance?