While living at Warburton, Dawson married a woman named Alkawari. They moved to Irrunytju, closer to Dawson's home country, and had three children during the 1970s. Dawson married again much later, to Anmanari Brown. Anmanari had also been married before, and her several children became part of his family. Dawson remained highly respected as a community elder and traditional healer until his death.