Al-Dawsari started his career in the youth teams of Al-Qadsiah. He was first called up to the first team on 12 April 2018 during the match against Al-Nassr, where he was an unused substitute. On 28 May 2018, he signed his first professional contract with the club.[5] On 29 August 2019, Al-Dawsari renewed his contract with Al-Qadsiah until 2024.[6]
On 7 August 2021, Al-Dawsari joined Al-Hilal on a five-year contract.[7] On 30 January 2022, Al-Dawsari joined Al-Fateh on loan.[8]