Kozorog won a silver medal in the C1 team event at the 2020 European Championships in Prague. She also won two silver medals in C1 team at an U23 level at the 2017 U23 Euros and 2018 U23 Worlds in Hohenlimburg and Ivrea, respectively. Alja earned her best senior world championship result of 19th at the 2019 event in La Seu d'Urgell, which secured Slovenia an Olympic quota. She finished in a career-best 4th place at the 2019 World Cup on her home course in Tacen.