This portrait was named Miss A Parker.
It is most likely Alice May Parker, the only daughter of Robert John Parker (c.1837-1903) and Jane Roberts (1839-1924). Alice was born in Launceston on 17 Jun 1869, never married and died aged 86 on 6 Feb 1955. Her cremated remains were interred with her parents at Carr Villa. Her mother Jane and brothers Robert and Percy are also pictured in the Launceston Family Album.
The other possibility is Agnes Mary Parker who was born on 17 Jan 1866, the third of seven children born to Edward George Parker (c.1837-1880) and his wife Agnes Long (Laing) Allan (1838-1878). Agnes moved to South Melbourne where she worked as a typist. On 19 Aug 1933 she died as the result of a car accident. She was the sister of Violet Maude Harrison, and Messrs Edward Allan, Arthur James and Allan T Parker. This family lived at 27 Trevallyn Road, Trevallyn, at the time of the Exhibition. Edward is also pictured in the Family Album.