The Korean government rejected Japan's proposal to take the question of sovereignty over Dokdo to the International Court of Justice. Japan threatened to take the issue without Korea's consent, but the ICJ needs the consent of both parties in anyp dispute to spring into action.
Although in 1965 the two countries signed normalization of their relations to resolve territorial row in accordance with a bilateral diplomatic note on settling disputes between the two countries, Japan's claims that Dokdo is a disputed territory has been excluded from the normalization documents. Therefore, there is no need to consent to the Japan's request to take the issue to the ICJ. Moreover, Dokdo is clearly Korea's sovereign territory, a fact that precludes the existence of any dispute over the islands. If both countries do not consent, the suit will not be proceeded. Therefore, Japan's action to take the issue to the ICJ by itself is simply hilarious.
Korea at the moment has a firm stance in the territorial dispute between the two countries. First, Korea has effective control over Dokdo, and there is no historical reason Japan should say that Dokdo is their territory. Therefore, Korea did not and felt no need to outwardly state that Dokdo is their territory. Simply stated, a person on the street wearing a Rolex watch wouldn't shout out to everybody that the watch indeed belongs to him because others would think that the watch implicitly belongs to that person. Just by shouting that, he would instead arouse suspicion. This is the case for Dokdo. Since Dokdo is Korean territory with 100% certainty, there is no need to turn it into a disputed territory. It is all Japan's trickery to turn Dokdo into a disputed territory so that they can have a shot at stealing something that does not belong to them.