Veit represented Slovenia at the 2008 Summer Olympics in Beijing, where she competed for the women's 200 metres. She ran in the third heat against seven other competitors, including United States' Marshevet Hooker, and four-time Olympian Debbie Ferguson-McKenzie of the Bahamas. She finished the race in fifth place by four hundredths of a second (0.04) behind Cyprus' Eleni Artymata, with a time of 23.62 seconds. Veit, however, failed to advance into the quarterfinals, as she placed thirty-fourth overall, and was ranked below four mandatory slots for the next round. She also tied her overall position with Barbados' Jade Bailey.