Children Of The Dust by Louise Lawrence
It doesn't seem real when the sirens go off and Sarah and the other children are sent home from school. But the nuclear attack is real enough, and it means that Sarah and her family have to stay cooped up inside for days on end. The world seems set to be choked by the grey dust that falls like snow from the sky, but Catherine, Sarah's younger sister, is determined to survive and build a new world from the ruins of the old.