Douris passed on the chance to play major junior hockey so that he could play at the University of New Hampshire at the age of 17.
The Winnipeg Jets took Douris 30th overall in the 1984 NHL Entry Draft. The Jets liked his skating ability, as he was fast and strong on his skates. He had a hard right handed shot which he often utilized from the left wing, giving him a better shooting angle on goalies. A good goal scorer in college and in the minor leagues, he was a modest scorer at the NHL, finding the net a total of 54 times. Though he had good size and strength, he was mostly a finesse player.
After two seasons at university, Douris decided to commit to the Canadian national team. Though he did this at the beginning of the 1985-86 season, he had the playing for Canada at the 1988 Calgary Olympics in mind. However Douris was convinced by the Jets that spending three full seasons with the national team would hurt his development and chances of ever making the NHL. He signed with the Jets in January, 1986 shortly after the World Junior Championships. He would play 11 games with the Jets to finish the season.
Douris apprenticed in the minor leagues in 1986-87, though it was loaned to Montreal's farm team in Sherbooke. Nonetheless he emerged as a key player as Sherbrooke made it all the way to the Calder Cup final. Douris led all AHL players in playoff assists and points but Sherbrooke would lose out to Rochester.
Douris would spend the next season playing with the Jets farm team in Moncton, continuing to put up strong numbers. But again he would find little chance of cracking the Jets line up, getting called up for just four games.
Douris was traded to St. Louis for the 1988-89 season, though he never played for the Blues. He played out the season and became a free agent.
Douris signed on with the Boston Bruins and would play in 148 games over the next four seasons. He also spent a lot of time shuttling back and forth from farm teams in Maine and Rhode Island.
Douris signed with expansion Anaheim as a free agent in 1993. It would mark the beginning of the longest period of stability. He would spend the next three full seasons in Anaheim. In the first two Douris was an everyday player. However an uncooperative groin injury cost him a lot of time in his third season with the Ducks.
The Ducks decided to walk away from Douris and his medical record in 1997. He would sign with the Dallas Stars, but only play in one final NHL game. Otherwise he spent the entire season back in the minor leagues.
Douris opted to bypass the buses of the minor leagues and headed across the pond to Europe. He would extend his career by playing four more seasons in Germany.
Douris retired and tried his hand at selling real estate and mortgages. But in 2013 he returned to both hockey and to Europe, becoming a junior coach and director of player development in Denmark.