It is clear that Dokdo has been the Korean territory since 512, the 13th year of kin Jizeung' reign of the Silla Dynasty, and the Japanese map expert, Hayasi Shihei(1738-93) also admits Dokdo is the Korean territory in his book, Samguktonglamdoseol written in 1785.
Putting aside Japan's imperialist aggression against Korea in the past, for both countries to go to the ICJ is unneeded and unhelpful as the court has no real authority to make the countries do anything. If the ruling is brought down against Japan, the government can simply ignore the ruling.
Secondly, the ICJ court does not take into consideration the concept of imperialist aggression, nor does it weigh judgments heavily on historical background. Prevent a grievous injustice and foreign tensions by urging Japan to back down.