Born in Brisbane, Dunemann grew up in Toowoomba, where he played his junior rugby league for the Newtown Lions and attended Harristown State High School.
In 1992, he started at halfback in Harristown's 16–17 Commonwealth Bank Cup final loss to Patrician Brothers' College, Fairfield.
His teammates from that team included his younger brother Andrew and future Australian and Queensland representative Steve Price.
He made his first grade debut in Round 1 of the 1995 ARL season, starting at five-eighth in the Cowboys' first ever game, a 16–32 loss to the Sydney Bulldogs, in which he kicked three goals.
[3][4] In 2006, Dunemann joined the Lézignan Sangliers, being part of the side that lost the 2006/07 Elite One Championship Grand Final.