Career
Dumić started his career in the Roskilde-based club Himmelev-Veddelev Boldklub along with Football Club Midtjylland striker Mads Hvilsom. Dumić joined the Norwich"s academy at the start of the 2008-2009 season having previously been signed with Hvidovre IF. On 22 June 2008, Dumić signed a professional contract with Norwich City. He has since been involved in a number of the club"s pre-season friendlies in the lead up to the 2009-2010 season.
On 14 January 2010, he moved back to Denmark, signing with Brøndby.
He made his debut for Brøndby on 23 August 2011 in an away game against Silkeborg. On 19 January 2016, he moved to Dutch club Nippon Electric Corporation on loan until the end of the season, with option to make it permanent.
In February, he signed on permanent basis, until June 2019. Dario played in all youth selections of Denmark, except senior.
However, he openly expressed his wish to play for Bosnia and Herzegovina on many occasions, even for a Danish sport channel, which became a real possibility as new Bosnia national team coach, Mehmed Baždarević, admittedly expressing great interest for the young defender, and even planned to visit Denmark, to watch Dario play and to speak with him face-to-face.