Given that Farquaad is only a lord, his land must be a vassal to a much larger kingdom. He may have sworn allegiance to King Harold, but another king (King Midas) was mentioned in Shrek Forever After. Do we know to which king he swore allegiance to?
The article about the Shrek "universe" on the Shrek Wikia has an apparently comprehensive list of locations in Shrek's world. This includes the movies and spinoff material, especially Puss in Boots. There are a significant number of locations that cannot be placed with any accuracy on even a schematic map. However, in spite of there being an awful lot of uncertainty about the world's geography, there is no evidence of a larger polity that includes Duloc.
In fact, the article concludes that Duloc appears to be an independent monarchy. This is perfectly reasonable; there is no reason that the ruler of an independent princely state needs to have the title of "king"/"queen" or "emperor"/"empress."
Historically, many de facto independent states ruled by counts, grand dukes, and such were nominally fiefs of a larger empire or kingdom. And power could ebb back and forth between the central suzerain and the outlying fief. But princes with lesser titles did not always need to have even a nominal overlord. Some monarchs, such as the Grand Dukes of Luxembourg, retained lower ranking titles even after their states gained complete de jour independence. Other monarchs, such as the Gediminid Grand Dukes of Lithuania, had never owed fealty to a higher temporal ruler.
In the case of Shrek's universe, geographical facts are really only decided upon in service of story plots or humor. The Wikia article also points out that the continuity contains numerous references to real-world locations, but no effort seems to have been made to harmonize the stories with real Earth geography.