I found out the answer. Boksu called her that because of her bubbly, scatterbrained personality. It's rendered "Dulli" in our subtitles, but the cartoon character he's referring to was Dooly, a baby dinosaur who was frozen in ice and unfroze in the 20th century, IIRC. The show was popular in Korea, in the 80s and 90s, I think.
From Seoul Selection, which sells Korean books, CDs, and DVDs (located in Seoul SK):
A little dinosaur Dooly, who was imprisoned in a giant iceberg in the South Pole thousands of millions of years ago, happens to be freed and floats down the Han river in Seoul. Doolie wakes up from his long sleep, and stays with an ordinary citizen, Mr. Ko Gildong. There, he gets into all kinds of mischief with his friends Heedong, and extraterrestrials Dona and Tochi, and his neighbor, Michael. Then the friends decide to become human adults by getting into alien Dona's time machine. However, the machine makes a mistake and they are lost in time and space.