Dobbin was first selected for the national rugby team in 1903, in the First Test of the 1903 British Isles tour of South Africa. South Africa had a poor international record to date, having played seven matches, all against the British Isles, and had won only one game. The 1903 tourists had a difficult campaign before meeting the South African national team, having lost seven of the 16 games against the invitational county and regional teams. Dobbin was brought into the South African team for the First Test, partnered at half-back with seasoned international Jackie Powell. The game was very tight, with both teams scoring two converted tries to leave the final score 10-10. Dobbin celebrated his first cap by scoring one of the two South African tries, converted by Fairy Heatlie.