Just so you know, I do not have any acces to Ancestry (cannot afford it) So I use Family search and the DIA BDM Records.
I found the passenger list for William - he travelled to NZ in 1872 at age 6 - with his widowed mother Anna, and his siblings - Elizabeth aged 9 and Frederick aged 2 - and yes the passenger lists says they disembarked at Napier.
In the 1871 census The family were living in Kensington, London, and there were 4 children. The mother Anne was from Wiltshire and was already widowed. The children were Elizabeth aged 8, William Henry aged 6, Adolphus aged 3 amd frederick George aged 1. Adolphus died in 1871 (After the census) at age 3, which is probably what prompted Anna to emigrate and find a better life.