Born in Skopje, Macedonia, Dorian joined Real Madrid's youth setup in 2011, after representing Gramanet and UE Cornellà.

[3] On 17 January 2022, he joined Debreceni VSC in the Nemzeti Bajnokság I, the top tier of Hungarian football, on a two-and-a-half-year deal.

[5] On 28 August 2023, he signed a two-year contract with Swiss record champions Grasshopper Club Zürich,[6] with an option to extend for a further year.

[7] Babunski was first called up to the Macedonian senior national team for their World Cup qualifier matches in November 2021, but did not see any playtime.

[8][9] On 2 June 2022, he finally made his senior debut for North Macedonia, in a Nations League match against Bulgaria, coming on in the 72nd minute of the game.