With the end of thread, a new period of exploration and expansion would begin. New holds would be founded, new land cultivated, new crafthalls established. There would likely be a steep rise in the population of humans. Since dragon reproduction is effected by Threadfall, there would likely be fewer, and smaller clutches. The localized system of government, with the Lord Holders overseeing their specific territory, and each Weyr having it's own leaders would likely continue. I believe, if the colonists were as intelligent as stated, they would not consider a centralized government. If you have a system that works, you don't throw it away.
As before, the Harper Hall would be the center of knowledge, and the harpers would act as arbitrators. The dragonriders would work with the harpers, as a police force, when needed. Leaders would meet in conclave to
exchange information as required, confirm boarders, negotiate trade agreements, etc.
With a larger population, more places to live and more work to be done, people would have the opportunity to move about with far more freedom. Every variety of group dynamics possible would likely occur, and each system would be exist or be replace depending on how well it worked. No one system of government would rise above the rest. If someone did not like how things worked where they were, they could try to effect change, move to somewhere else, or find a place of their own.
Pern would be a world of endless frontiers and possibilities, with no stifling "world government" to oppress and restrict the populace.