He debuted for Queensland against a visiting New Zealand team in 1959 and was selected in the Australia national rugby league team for the same series. He also played in the Queensland victory over New South Wales that attracted 35,261 spectators, smashing Brisbane's previous record for an interstate match of 22,817. Muir then made his Test debut on 13 June 1959 at the Sydney Cricket Ground along with Reg Gasnier, Johnny Raper and Noel Kelly and played in all three Tests against the Kiwis. Later that year was selected for the 1959-60 Kangaroo tour where he appeared in all six Tests and fourteen minor Tour matches.