Dowd was selected by the Los Angeles Kings in the seventh round (No. 198) in the 2009 NHL Draft after playing for Wenatchee of the North American Hockey League. The following season, he played for Indiana of the United States Hockey League and had 39 points (16 goals, 23 assists) in 46 games.
Dowd played the next four seasons as a forward for St. Cloud State University, where he had 121 points (52 goals, 69 assists) in 155 games. He was named to the All-National Collegiate Hockey Conference First Team and was a finalist for the 2014 Hobey Baker Award, awarded to the top player in NCAA Division I hockey.