Races of the Dragon certainly indicates that dragonwrought kobolds are rather rare in kobold populations. It does not appear that they breed true.
Moreover, Races of the Dragon defines both dragonwrought kobolds and half-dragons as “versions” of full dragons. But the parent of a half-dragon is the full dragon. Even if a red-dragonwrought kobold or a red half-dragon are “versions” of a red dragon, even if they count as a form of “true dragon,” the parent of a red half-dragon is a red dragon—not any other “version” of it. So the offspring of dragonwrought kobolds (and half-dragons) is not a half-dragon.
The fact that the half-dragon template is much stronger than the Dragonwrought feat, and offers numerous dragon-y features that dragonwrought kobolds lack, is another strong reason to believe dragonwrought kobolds do not give birth to half-dragons (barring a full dragon mate).
Thus, the most common progeny of a dragonwrought kobold seems likely to be regular kobolds, though dragonwrought kobolds are presumably more likely for them than for other kobolds. Perhaps a mating pair of dragonwrought kobolds would be able to reliably produce more dragonwrought kobolds. I do not believe that Races of the Dragon addresses the point directly.
As for half-dragons, since I brought them up: the draconic template in Races of the Dragon is most likely the best choice for the offspring of half-dragons (assuming the other parent is not a dragon of any kind).