[6] Donoghue was elected to the ICJ on September 9, 2010, to fill the place left vacant by the resignation of Thomas Buergenthal.

Pursuant to the Statute of the International Court of Justice, Donoghue completed the remainder of the nine-year term for which Buergenthal had been elected, which expired on February 5, 2015.

As an ICJ judge, she issued a dissenting opinion in the case Legal Consequences of the Separation of the Chagos Archipelago from Mauritius in 1965, in which the ICJ issued an advisory opinion in 2017 on the Chagos Archipelago sovereignty dispute between the United Kingdom and Mauritius in response to a request from the United Nations General Assembly.

The court deemed the United Kingdom's separation of the Chagos Islands from the rest of Mauritius in 1965, leading to the expulsion of the Chagossians when both were colonial territories, to be unlawful.

[13] Judge Donoghue dissented from the majority opinion, reasoning that:I consider that the Advisory Opinion has the effect of circumventing the absence of United Kingdom consent to judicial settlement of the bilateral dispute between the United Kingdom and Mauritius regarding sovereignty over the Chagos Archipelago and thus undermines the integrity of the Court’s judicial function.