hi Baz,
PRO Vic has the family in their unassisted passenger lists. F refers to the port of arrival, but I don't know which one.
DAVIES HENRY 28 DEC 1889 ERLANGEN F 255 001
DAVIES MARY 15 DEC 1889 ERLANGEN F 255 001
DAVIES EDWARD 11 DEC 1889 ERLANGEN F 255 001
DAVIES TYWYMA 9 DEC 1889 ERLANGEN F 255 001
ROBERTS DAVID 38 DEC 1889 ERLANGEN F 255 001
ROBERTS ANNA 35 DEC 1889 ERLANGEN F 255 001
ROBERTS ARNEA 6 DEC 1889 ERLANGEN F 255 001
ROBERTS MARY 4 DEC 1889 ERLANGEN F 255 001
ROBERTS GRIFFITH 2 DEC 1889 ERLANGEN F 255 001
ROBERTS MAGGIE 1 DEC 1889 ERLANGEN F 255 001
So to re-cap: Griffith D Davies went to Ballarat sometime after the 1881 census, probably after his daughter’s 1882 marriage to David Roberts, and then returned to Tywyn, dying there in 1886. His three eldest sons were in Australia, probably NSW by 1887. David and Anne E Roberts emigrated in 1889 aboard the Erlangen taking Anne’s four youngest siblings with them. Their mother remained in Tywyn. Quite a story there somewhere!
Here is a snip from the manifest of the Selkirkshire, arriving Sydney 13th Jan 1884, recording a £4 assisted passage for Griffith Davies aged 21, skinner / wool stapler from Merioneth. The age certainly fits Anne Elizabeth’s eldest brother, Griffith Ch Davies, although he was recorded as a pupil teacher in the 1881 census. If it's his father then about 40 years have been lost in transit!