Despite the potential economic and environmental consequences of uranium mining in Kakadu National Park, and the agreement that national parkland shouldn't be exploited for its resources, it is ultimately (ethically) the government's purview to use the land the way it sees fit. Uranium is a rare resource, and if the Australian government believes mining in the park would produce the greatest net benefit for its people, there is no ethical reason why they shouldn't be allowed to.
The Australian government shouldn't mine for uranium in Kakadu National Park because it's a national landmark and preserve. Such areas should be preserved around the world in order to keep habitats intact and viewable by future generations. By mining for uranium here, the Australian government is destroying precious land that won't come back anytime soon.