Arunović became interested in shooting because of her older sister Jelena. She began to train in 2001 at the shooting club Policajac, and later moved to SK Crvena Zvezda.
She won silver team medal in Junior event at the European 10 m Events Championships in 2004 in Győr, and bronze team medal the following year in Tallinn, respectively. She won individual and team gold in the same event in 2006 in Moscow. Later in the year, Arunović won individual gold in 25 m pistol and team bronze in 10 m air pistol in Junior events at the 2006 World Shooting Championships in Zagreb. At the 2009 Mediterranean Games in Pescara, she won gold medal in 10 m air pistol.
Arunović made breakthrough in 2010, when she won individual gold medal in 10 m air pistol, and both individual and team silver in 25 m pistol, alongside her sister Jelena and legendary sports shooter Jasna Šekarić, at the 2010 World Shooting Championships in Munich. The win also made her the first woman athlete to secure quota for Serbia for the London 2012 Summer Olympics. In September 2010, she climbed to first place in the ISSF world ranking in women's 10 m air pistol.[1] At the end of the year, she was named Serbian Sportswoman of The Year by the Olympic Committee of Serbia.[2] Arunović received Serbia's sport association "May award" in 2011. She won a silver medal in 25 m pistol at the 2011 Summer Universiade in Shenzhen.
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