Davidovac started to play basketball in the youth ranks of his hometown's Proleter Naftagas. In the 2011–12 season, he played his first Serbian League season. In 2012, Davidovac signed for Vršac Swisslion.
Davidovac signed for Crvena zvezda and was immediately loaned to FMP in March 2015, just before the start of the Serbian Super League season.[1] On 30 September 2016, Davidovac made his Adriatic League debut for FMP in a 78–76 loss to KK Zadar, making 7 points, 7 rebounds and 3 assists.[2] On 11 February 2017, Davidovac scored an Adriatic career-high 28 points to help defeat Union Olimpija.[3] Through 26 Adriatic League games in the 2016–17 season, Davidovac averaged 10.0 points, 5.1 rebounds, and 2.5 assists per game.[4]
On 13 September 2017, Davidovac signed a four-year contract with the Crvena zvezda.[5] On 22 October 2017, Davidovac made his debut for Crvena zvezda in the Adriatic League against Cedevita, making his 3 points, 3 rebounds and 2 assists in 9 minutes of playing time.[6] Two days later, on 24 October, Davidovac made his EuroLeague debut against Russian team Khimki, making two 2-point attempts and a rebound in under 6 minutes of playing time.[7] Through 23 games in the 2017–18 Adriatic season, he averaged 5.6 points, 3.1 rebounds, and 1.9 assists per game.[8] In 24 EuroLeague games, he recorded 6.5 points, 2.0 rebounds, and 1.2 assists per game.[9] Through 17 games in the 2018 Serbian SuperLeague season, Davidovac averaged 7.9 points, 3.9 rebounds, 1.6 assists, and 1.4 steals per game.[10] He won Serbian SuperLeague in the 2017–18 season. Davidovac averaged 6.2 points and 2.9 rebounds per game during the 2019–20 ABA season. On 8 September 2020, Davidovac signed a two-year contract extension with the Zvezda.[11][12]