This is not significant.
The Council of Elrond was not convened in order to choose members of a Fellowship, but rather to discuss the matter of the Ring. Choosing members of the Fellowship was just something that happened after Frodo volunteering to take the Ring to Mordor, and the members were chosen from those who were in Rivendell at the time.
Glóin and Gimli just happened to be the Dwarves who were there (as ambassadors from Dáin), and therefore Gimli was the one chosen by Elrond (Glóin presumably being too old):
For the rest, they shall represent the other Free Peoples of the World: Elves, Dwarves, and Men. Legolas shall be for the Elves; and Gimli son of Glóin for the Dwarves. They are willing to go at least to the passes of the Mountains, and maybe beyond. For men you shall have Aragorn son of Arathorn, for the Ring of Isildur concerns him closely.
The fact that those chosen for Elves and Men happened to be heirs is not relevant; Elrond was perfectly willing to choose other Elves who were not heirs or the final two members (before Merry and Pippin came onboard):
'There remain two more to be found,' said Elrond. 'These I will consider. Of my household I may find some that it seems good to me to send.'
Finally I should note that you're downplaying the rank of Gimli; as the son of Glóin he is also the son of one of the Dwarves who did the Quest of Erebor, and the son of an ambassador from one of the greatest Dwarf kingdoms, as we learn when Glóin is first introduced:
Next to Frodo on his right sat a dwarf of important appearance, richly dressed. His beard, very long and forked, was white, nearly as white as the snow-white cloth of his garments. He wore a silver belt, and round his neck hung a chain of silver and diamonds.