Døssing was born in Viborg, Jutland and started his career with his hometown club Viborg FF in 1958, aged 17. With the help of Jack Johnson, a former manager of B 1913, Døssing got in contact with Dundee United.
Døssing's football journey began with his hometown club, Viborg FF, in 1958 when he was young. He was connected to Dundee United by Jack Johnson, a previous manager of B 1913.