Compared to some Empires, 120k is tiny
To put into comparison how feasible this is, we just need to take a look at the Roman Empire.
In 25 BCE, the estimated area of Rome was about 1,060,000 square miles or about 2,750,000 km^2.
This was long before medieval times, so if it was possible then, why wouldn't it be possible in a setting that is even further in the future?
Other massive empires included the Mongol Empire, which was even larger in comparison. In 1309 it is estimated to have had about 24,000,000 km^2 area (which is about 9,300,000 square miles).
If the Mongols and the Romans were able to pull off empires that were significantly larger than this, then it is certainly feasible.
The Mongols are often considered the largest land-based empire in history, second only to the British Empire, and the British Empire had the advantage of technology that was definitely not available to the Mongols. If you are looking for the largest an empire can be with only medieval technology, the Mongol Empire is, historically speaking, as large as it can get.
You also have the advantage that this is an island locked in by the ocean. Once you've conquered all the lands within the island, the people either have to accept the rule or hope they can somehow take a boat to another land.
As for the question of, "would it dissolve into smaller kingdoms?" that depends on a lot of factors.
Generally speaking, empires break into smaller bits because they have overextended themselves. If they don't have the manpower or infrastructure to maintain such a massive landmass, then it will eventually break into pieces, but an island of this size could remain relatively stable. While massive empires crumble easily, a reasonably-sized nation with decent leadership can last a very long time.
Another factor is culture. The people of the island might not want to be under the thumb of an emperor in the first place. For example, there might be hundreds of languages and religions on the island, but the empire only wants one language and one religion. This could lead to the island dividing into several smaller nations and cultures.