Dunham represented New Zealand at the January 2013 Australian Youth Olympic Festival in Sydney, Australia. In the single sculls, he came 15th out of 18 competitors. In the quadruple sculls, he won a bronze medal with his team. In the eight, he won a silver medal. He also competed at the July 2013 Summer Universiade in Kazan, Russia. His first international appearance at a FISA regatta was at the 2014 World Rowing U23 Championships in Varese, Italy, where he came ninth in the U23 lightweight double sculls partnered with Toby Cunliffe-Steel. At the 2015 World Rowing U23 Championships in Plovdiv, Bulgaria, he came fourth in the U23 lightweight double sculls partnered with Bryce Abernethy. Dunham went to the 2016 Summer Olympics in Rio de Janeiro, Brazil, as a reserve for the lightweight men's four but did not compete.