So, and correct me if I'm wrong, from what I understand, being dragonborn means being born with the soul of a dragon. And we know that when you kill dragons you absorb their souls. My question is this: if a dragon were to kill another dragon, would it then absorb the other dragon's soul? Or is that ability exclusive to the dragonborn?

Nope, that's the Dragonborn's thing.

Or maybe Dragons eat our souls while we absorb theirs... lol....

i wonder if souls taste good with mudcrab meat...