James Dredge was born about 1839 in Wincanton, Somerset, the son of John Dredge and Elizabeth Stone. John Dredge was the son of Peter Dredge, carpenter, of Britford, Wiltshire and his wife Ann White from Oddstock, Wilts. John Dredge had two brothers: James, b 1796 in Britford, emigrated to Australia in 1839 when he was appointed Assistant Protector of Aborigines, and Peter, b 1812, Carpenter, followed his elder brother to Melbourne, Victoria, Australia in 1840. Up to 1905 all the Dredges recorded in the Victorian BDM indexes were descended from James or Peter Dredge.
Your ancestor James Dredge who emigrated to New Zealand would have been the nephew of James and Peter Dredge in Melbourne, Australia.