He played Tier II junior hockey for the Newmarket Flyers, Nepean Raiders, and Smiths Falls Bears and major junior with the Kitchener Rangers. Undrafted by any NHL team, Dopson joined the Wilfred Laurier Golden Hawks in 1987 for three years.
In 1991 he was signed as a free agent by the Pittsburgh Penguins. He played 2 games for them in 1993-94 but spent most of his time in the minor pros. In 1997-98 he played a season in Great Britain for the Ayr Scottish Eagles. The next season he went to Japan and played for the Nippon Paper Cranes until his retirement in 2002.