In August 2001, Cojocar competed in the Goodwill Games in Brisbane, Australia. She won the all-around title, upsetting more established gymnasts, such as Russia's Svetlana Khorkina, and earned a bronze medal on the floor exercise. Her first major senior event was later in the year at the 2001 World Championships in Ghent, Belgium, where she placed first with the Romanian team, sixth in the all-around, and fourth on beam.