He started his international career at a young age, winning his first discus title at the age of fifteen at the 1996 Asian Junior Athletics Championships. He won at the Pan Arab Junior Championships two years later and made his global level debut at the 1998 World Junior Championships in Athletics, where he was eighth overall. Al-Dosari was one of the most promising Qatari athletes to emerge at the time, as the small nation was not renowned for producing track and field athletes. He retained his Asian Junior title the following year and also won his first senior titles, with gold medals at the Pan Arab Championships and 1999 Pan Arab Games.