It seems that Alberta went to New Zealand with other members of the Eccles family. There is a probate record for a Samuel Eccles, a tailor, in New Zealand, which is almost certainly Alberta's father. There are also the marriage records for Alberta's sisters Clara Ella and Alma in New Zealand. Clara Ella was married in 1874 and Alma in 1875. The family are on the 1871 UK census so they must have moved to New Zealand some time between 1871 and 1874.