Dodd attended Byrnes High School and was the starting quarterback for three years there. During his sophomore campaign, his first as a starter, he threw for 3,202 passing yards and 32 touchdowns. He set the school record for most passing yards in a game on October 5, 2007, when he had 462 against Hillcrest. In his junior year, Dodd passed for 2,927 yards and 28 touchdowns. In his senior year, he established a Byrnes HS record with 4,163 passing yards during the season, while completing 252 of 391 passes with 51 touchdowns. Overall, Dodd threw for 10,640 yards in his high school career, which was the highest total in school history. He had a 42–3 record as a starter and led his team to two state championships.
College
Dodd committed to Rutgers University in July 2009. As a true freshman in 2010, Dodd did not play much during the first few games of the season. On October 8, however, he made his first career college start against Connecticut, as fellow quarterback Tom Savage was injured. In that game, Dodd threw for 322 yards and two touchdowns, and Rutgers came back in the fourth quarter to defeat the Huskies 27–24. Dodd was named Big East Offensive Player of the Week. During the next game, against Army, Dodd directed another fourth quarter comeback. He had 251 passing yards and two touchdowns; Rutgers won in overtime. Dodd saw most of the action at quarterback during the last six games of the season, but Rutgers finished with six consecutive losses. On November 20, he threw for a season-high 335 yards and four touchdowns against Cincinnati in a 69–38 defeat. The four touchdowns set a Rutgers single-game record for a true freshman. For the year, Dodd had 1,637 passing yards, 11 touchdowns, and seven interceptions, and he led the team in all three categories. Dodd started 8 games at quarterback for Rutgers during the 2011 season, however as the season went on Freshman Gary Nova started taking on a greater role at the position He finished the season with 1574 passing yards, 10 touchdowns, and 7 interceptions During the 2012 season Dodd performed in a backup role to Nova, playing a total of 3 games and throwing a total of one pass. Despite the lack of playing time he was named to the Big East All-Academic Football Team which recognized players who excel in the classroom as well as on the field.
Professional
Dodd has continued playing football professionally signing a contract to play for the Lazio Marines of the Italian Football League. He is one of two Americans permitted to play on the team per IFL regulations.