Golubović made his Slovenian PrvaLiga debut for Domžale on 21 May 2016 in a game against Krško.[1] On 6 November 2018, he was released from his Catanzaro contract by mutual consent.[2] On 2 July 2019, he then signed with Serie C club Vis Pesaro for one year, with the club holding an option to extend the contract for another year.[3]
On 11 January 2020, Golubović was loaned out to Bosnian Premier League club Sloboda Tuzla.[4] In July 2020, he joined the club on a permanent contract.[5] In May 2021, Golubović left Sloboda.[6]
Before the start of the 2023–24 season, Golubović moved to Romanian Liga I club Dinamo București.[7] He started the season as the first-choice goalkeeper, and recorded his first clean sheet on 14 August in a 1–0 victory against FC Botoșani.[8]