Harry McQueston was born on August 4, 1916, in Toronto, Ontario. Of Irish parentage he started at an early age to excel in hockey and soccer. While being an outfield player in soccer he was a goalkeeper in hockey.
In the summer of 1936 Harry won the Western Section of the National Soccer League with Ulster United. The Redhanders qualified for the NSL Championship final but lost to Montreal Carsteel.
In 1936 Harry joined Toronto Goodyears in the Ontario Hockey Association. He stayed with the Goodyears for four season.
The 158 lbs inside forward spent the 1938 summer playing for England United in the National Soccer League.
In 1939 Harry joined the Atlantic City Seagulls in the Eastern Amateur Hockey League.
Before the start of the 1944-45 National Hockey League season Harry was scheduled to have a try out for Toronto Maple Leafs. However, while playing soccer for Ulster United he broke his wrist late in in the season, and missed out on his chance to play for the Maple Leafs.
After recovering from his injury Harry started the 1945-46 hockey season with Providence Reds in the American Soccer League. In February 1946 Minneapolis Millers of the United States Hockey League purchased Harry from the Providence Reds.
The inside forward won the Dominion Championship with Ulster United in 1946.
Harry returned to the Millers for the 1946-47 season and signed a new contract on September 30, 1946. He was the leading goalkeeper in the USHL with five shutouts. He stayed with the Millers until the end of the 1949-50 season. By January 1950 he was the league leading goalkeeper with a goals against average of 3.31. He was traded to the Cleveland Barons but, after one game, he was traded from Cleveland to Detroit Red Wings in the National Hockey League. It was said that he would be shipped to Omaha by the Red Wings. However, the 33-year old goalkeeper returned to the Barons.
On May 24, 1947 he played for Ulster United against the German-American League All-Stars in New York. 3,000 soccer fans watched as Harry scored two goals to lead Ulster United to a 3-2 win.
Well into his veteran stages Harry spent the winter of 1952-53 playing in the Scottish National League with the Fife Flyers.