Dodt joined the Asian Tour for the 2008 season, finishing his début season ranked 43rd on the Order of Merit, and improved to 15th in 2009. He won his first professional tournament at the 2010 Avantha Masters, which was co-sanctioned with the European Tour.
In 2015, Dodt won on the European Tour for the first time in five years at the True Thailand Classic, with a one stroke victory over Scott Hend and Thongchai Jaidee. He came from four shots behind in the final round with a five-under-par round to claim the victory.
Dodt showed a return to form at the end of 2016, finishing runner-up in the Australian PGA Championship and tied for third in the UBS Hong Kong Open, in successive weeks. In 2017 he had some good results in important events, finishing tied for 6th place in the 2017 BMW PGA Championship and tied for 4th in the Aberdeen Asset Management Scottish Open.
His good Scottish Open finish qualified him for the 2017 Open Championship where he finished tied for 44th place. 2018 was a disappointing year; his only top-10 finish being in the Fiji International.
Dodt injured his back in April 2019 and only returned to competitive golf in August at the Sarawak Championship. Dodt won the event after a playoff with Richard T. Lee.