Dagný started playing football when she was six years old, with her first club, KFR from Hella and Hvolsvöllur. She played for them in 2006 as they competed in a joint effort with Ægir from Þorlákshöfn. Since 2007 she has played for Valur from Reykjavík in the best women's league in Iceland, Úrvalsdeild. In 2011 Dagný began attending Florida State University and began playing for Florida StateSeminoles. She returned to Iceland to play for Valur during the summer months.
Florida State Seminoles, 2011–2014
Dagný attended Florida State University where she was a four-year starter from 2011–2014 for the Seminoles in the midfielder position. She helped lead the Seminoles to a national championship in 2014. Dagný holds the school record for 19 game-winning goals and is second in total goals, shots, and points. She was a first team All-American in 2014 and the runner-up for the MAC Hermann Trophy, given annually to the best college female soccer player. She was named Soccer America 2014 Women's Player of the Year. She was also named as a first team Scholar All-American by the National Soccer Coaches Association of America.
In 2014, Dagný played for Selfoss. In 2015, she signed for the second half of the season to the German Frauen-Bundesliga team Bayern München.
Portland Thorns, 2016–2019
After her career at Florida State, Dagný did not sign up for the 2015 draft to play in the National Women's Soccer League in the United States. In May 2015, she attempted to play during the 2015 season with the Western New York Flash, but was prevented from doing so by league rules. In October 2015, the Portland Thorns FC announced that they had acquired rights for her from the Boston Breakers and that she would play for the Thorns in the 2016 NWSL season. After spending the 2016 and 2017 seasons with the Thorns, it was announced that Dagný would miss the 2018 season due to pregnancy. She gave birth in June 2018 and returned to training with the team in March 2019.
Selfoss, 2019–present
In 2019, Dagný returned to Iceland and signed with Selfoss.
International career
Dagný made her debut for the senior Iceland national football team at the 2010 Algarve Cup; in a 2–0 defeat to the United States on 24 February 2010. She was called up to be part of the national team for the UEFA Women's Euro 2013. In Iceland's final group match against the Netherlands, Dagný headed the only goal of the game to secure her team's place in the quarter-finals. It later emerged that she had played the game with a broken foot, sustained in the previous match against Germany.
Personal
Dagný gave birth to son Brynjar in June 2018, making her one of several mothers playing in NWSL. She subsequently married the father, Omar Pall, in July 2019.