Dundas started his career with Dundee side, Perseverance F.C., in 1883. The club had joined the S.F.A. for the start of the 1882-1883 season, and played their matches at Angus Park, Dens Road, which had previously been farmland.
In 1886 Jimmy joined Forfar Athletic. A local lad, he was a popular member of the team, becoming vice-captain of the team. At 5 ft 7”, and weighing 11 stone, he was described as “a sturdy and hardworking centre forward. He passed, with good judgement, and did not hesitate to let fly at goal.”
His next club was Our Boys, joining in 1891 and spending the next two seasons with them.
On the amalgamation of Our Boys and East End in 1893, Jimmy joined the newly formed Dundee F.C. He scored the second goal for Dundee, a header (from a Dundee free-kick), in their first league match at West Craigie Park, against Rangers on 11th August . The match ended in a 3-3 draw.
When Alick Craig became the favoured player in the forward position, Dundas moved to right half back. It was to be the position he played for the rest of his career.
On the 15th February 1896, Jimmy was selected to represent Scotland, at Celtic Park, in an Inter League International between Scotland and Ireland, which ended in a 3-2 win. It was to be his only International call-up.
Throughout his time with Dundee F.C. interest had been shown from south of the border, but in 1897 he made the move north to join Victoria United. This was to be his last club before retiring. However, he was to stay involved in football, moving back to Dundee and working with William “Plum” Longair as his Assistant Trainer. He also took up Linesman duties on a regular basis at Dens Park.
Dundas died at the relatively young age of 48 in 1916, he had been ill for a considerable time, leaving a wife and three daughters. His son, Albert, an Able Seaman in the Royal Navy Volunteer Reserve, died at Galipolli in 1915 aged 21.