Davis earned FSWA All-State Class 3A first-team honors as a senior quarterback and was an honorable mention as a junior. He threw for 2,758 yards and 28 touchdowns in 2006. He completed 16-of-33 passes for 271 yards and one touchdown in the Kathleen High School's regional semifinal loss to Hardee. He completed 136-of-227 passes for 1,659 yards and 11 touchdowns as a junior, leading Kathleen to a 10–3 record and the district title. He also competed on the school's basketball and track and field teams.
College career
Boston College
After sitting out the 2007 season with Matt Ryan leading the Boston College Eagles, in his second season he and Chris Crane vied for the position of quarterback early on in the 2008 season. Dominique got his first snaps in a game against University of Central Florida following a poor showing by Crane. He also played in the following game against University of Rhode Island, but then was benched by head coach Jeff Jagodzinski as Crane solidified his position. Then in week 13 against Wake Forest Chris Crane went down in the second quarter and Dominique Davis came in with a 13–0 lead. Davis played mediocre, fumbling twice as the Boston College defense kept the game close until the final minutes of the game. Then with less than 4 minutes left Davis completed a long 3rd down to WR Rich Gunnell to put BC into scoring range. Following a pass to WR Brandon Robinson, Davis capped the drive with a short run for the winning score. His first victory as a starter came on November 28, 2008. The 28–21 victory over the Maryland Terrapins clinched BC's spot in the 2008 ACC Championship Game.
Davis was suspended for academic reasons in June 2009 and decided to transfer. On July 26 he announced his decision to transfer to Fort Scott Community College, where his plan was to play for one season before transferring back to a Division I program. He chose to transfer to East Carolina University and enrolled in May 2010. Davis helped lead Fort Scott Community College to its first Jayhawk Conference championship since 1974, defeating Butler Community College in the final game of the regular season. Butler had won the previous eight Jayhawk Conference championships. It was the first time FSCC had beaten Butler since 1986. Two weeks later, in a rematch, Davis' FSCC team defeated Butler, 13–12, to give the Greyhounds their first-ever Region VI Playoff championship. The Greyhounds were given the No. 1 ranking in the national poll and were matched up against No. 2 Blinn College for the National Junior College Athletic Association national championship in the Citizens Bank Bowl on the campus of Pittsburg State University. Blinn rallied from a 26–10 deficit in the second half to win the game 31–26 on an 84-yard punt return with 15 seconds remaining. Fort Scott's 11–1 final record was still its best since going undefeated to win the 1970 national championship.
East Carolina University
Davis transferred to East Carolina University for the 2010 season. In his first start with the Pirates, Davis completed 27 of 46 passes for 383 yards with 5 touchdowns and 1 interception. He also rushed for 29 yards with 1 TD. With five seconds remaining in regulation, Davis threw a 33-yard Hail Mary pass to Justin Jones in a 51–49 win over Tulsa. Davis went on to pass for 3,967 yard and account for the third most touchdown passes by a quarterback in the Football Bowl Subdivision and led the Pirates to a 6–7 record and a berth in the 2010 Military Bowl, losing 51–20. For the 2011 season Davis was named to the Manning Award, Maxwell Award, and Davey O'Brien Awardwatch lists. On October 22, 2011 the East Carolina quarterback did not throw an incomplete pass in the first half of the Pirates 38–35 victory over the Navy Midshipmen. This gave Davis the NCAA record for most consecutive completions in one game held by Tee Martin of Tennessee in 1998. Combining the 10 consecutive completions from the ECU's previous game against Memphis, his 36 consecutive passes over two games eclipsed the previous overall consecutive completion record of 26 held by Aaron Rodgers of Cal in 2004. This performance led Dominique to be selected by ESPN analysts as one of four finalists in the AT&T All-America Player of the Week for week 6 of the 2011 season. Davis is East Carolina's career leaderin passing touchdowns. He is fifth on the school's all-time passing yards list.
Professional career
Atlanta Falcons
Davis signed a deal with the Atlanta Falcons after going undrafted and reunited with his former teammate, Matt Ryan. Davis was named the third-string quarterback position, behind Ryan and Luke McCown. He was waived on June 19, 2014.
Davis signed a contract with the Calgary Stampeders on February 24, 2015. On June 20, 2015 Davis was released during the 2015 Calgary Stampeders training camp. in 2016.
Davis signed a contract with the Winnipeg Blue Bombers on June 29, 2015. In his first two seasons in Winnipeg he played in only one game, completing 16 of 25 pass attempts for 169 yards. On January 4, 2017, Davis was signed to a contract extension by the Blue Bombers. Davis played in three games in 2017, completing 17 of 29 pass attempts for 208 yards. On February 1, 2018 the Bombers announced they had released Davis.
Ottawa Redblacks
On February 12, 2018 Davis signed with the Ottawa Redblacks, replacing Drew Tate as the backup quarterback to Trevor Harris. In 2018 as a backup and short yardage rusher, Davis scored for the first time in his professional career; he completed 24 of 39 passes for 373 yards and 3 touchdowns against one interception, while producing 40 rushes for 73 yards and 6 touchdowns. He also started the final regular season game of the year against the Toronto Argonauts. Prior to free agency opening, Davis signed an extension with the Redblacks. When the Redblacks were unable to resign starter Harris, Davis became the assumed starter. However later in the off-season the Redblacks signed free agent pivot Jonathon Jennings to a higher salary to compete for the starting job. Nevertheless, Davis was announced as the starting quarterback for Week 1 of the 2019 season. After winning the first two games of the season, the Redblacks lost the following two games and Davis picked up a minor injury, which lead to Jennings being announced as the club's starting quarterback for the team's Week 6 match. Davis missed two games while recovering from his injury, and returned to action in Week 8. Davis was benched in the first quarter of Redblacks' Week 11 loss to the Saskatchewan Roughriders after throwing three interceptions in his first six pass attempts. Jennings was announced as the starting quarterback following the team's bye week. After both Jennings and third string quarterback William Arndt struggled the Redblacks turned to Jennings for the final game of the season. The Redblack's finished the year with 3 wins against 15 losses; the only wins came in the first half of the year with Davis as the starting quarterback.