She previously played for Bayern Munich, Portland Thorns, Selfoss, and collegiate soccer for the Florida State Seminoles.

[10][11] In 2019, Dagný left the Thorns, citing the difficulty of raising her son so far away from her home nation and family, and returned to Iceland to sign with Selfoss.

[14][15] She made her debut for the club in a 2–0 home defeat in a league match against Chelsea on 7 March 2021[16] She ended her first season campaign with 9 appearances across all competition with no goals.

She then scored West Ham United's extra-time winner at Reading in the FA Women's Cup fifth round on 27 February 2022.

[16] Prior to the start of the 2022–23 season, Dagný switched her kit number from 32 to 10, following the departure of Kateřina Svitková from the club in the summer.

[19] On 8 March 2024, West Ham United released their original documentary, Ómarsson,[20] which tells the story of Dagný's journey with pregnancy as a professional sportswoman and the barriers faced by female athletes when making the decision to start a family.

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.

[22] 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.