"A Royal Good Time" is a cartoon from RKO starring Otto Soglow's creation, the Little King. I've seen a few of them and must say that this is far from one of the better Little King cartoons (that would be the adorable "Christmas Night"). The animation is weak, the premise is weak and the portion with the African Dodger* is in very poor taste.
In this film, the Little King slips away from his palace to enjoy a carnival. Mostly instead of plot, it involves the King going from one vignette after another until a turban-wearing man inexplicably gives chase. So, as you can guess...not a whole lot in the way of plot.
*An 'African Dodger' was a very distasteful carnival game in which folks paid to throw balls at a black man who put his head through the back wall of the pavilion!