Doan was drafted by the Winnipeg Jets in the first round, seventh overall, in the 1995 NHL Entry Draft. He was the Jets' final first-round pick to play in the NHL prior to the franchise moving to Phoenix. He immediately made the transition from major junior to the NHL in 1995–96 and tallied 17 points in his rookie season with the Jets. He scored his first NHL goal against Ed Belfour of the Chicago Blackhawks, and later scored the overtime goal to win the game 6–5. Perhaps Doan's most memorable moment as a Jet was his seventh and final goal as a Jet, which came on April 12, 1996, during the team's last regular season home game, where he scored the game-winning goal against the Los Angeles Kings in the second period to make the score 4–2 for Winnipeg. The game would finish 5–3 and the win clinched a playoff spot for the Jets. In the playoffs, the Jets were matched up against the first seeded Detroit Red Wings and lost in six games.