She played for Slovakia in the 2010 Olympics. It was the first time that Slovakia competed in women's ice hockey outside of Europe. Her first Olympic women's ice hockey game came on February 13, 2010, against the team representing the country of her birth, Canada. Slovakia lost the game by an 18-0 mark and Babonyova was penalized for cross checking in the second period. Her first Olympic point came on February 15 in a 6-2 loss to Sweden. She finished the Olympic tournament with an eighth place finish.