Henry White had been employed as a surgeon in London. He was involved in the South Sea Company and was accused of forging signatures. His trial took place at the Old Bailey on 15th September 1825 and he pleaded guilty to the lesser of three charges of forging a signature of a witness and was sentenced to 7 years transportation. 
Henry White arrived in Hobart on the Earl St. Vincent on 13 August 1826. The Hobart Town Gazette reported - We congratulate the Colony on the arrival of the prisoners by the ship Earl St. Vincent. Never before, we may safely say, has such an accession to the labouring population arrived by any transport, of which the chief part consists of either farming men, or useful mechanics. The greatest credit is due to the Superintendent and to the Commander of the vessel, as out of the 260 not one has died on the voyage, and only two were sick on the arrival. The famous Dr. Henry White, of London, whom many of the colonists from that city will recollect, is a passenger by this vessel.
He was transferred to New South Wales on the Portland in September 1826.
He was first sent to a government farm at Emu Plains
He was assigned as assistant surgeon to an expedition to Western Port. The Westernport Settlement was established on November 24th, 1826 and abandoned on February 27th, 1828
Western Port Expedition
(Extract of a Letter, written by a gentleman on board the Dragon, at Western Port, dated Dec. 27, 1826 to his friend at Sydney.)
We performed our voyage from Sydney to this place in sixteen days, having experienced some strong gales and heavy weather, which compelled us to put into Twofold Bay, as also into Sealer's Cove. The Amity parted company, and we did not fall in with her afterwards; but suppose she proceeded at once to her destination. The advantages expected to be realised from this place I venture to predict, will never accrue, they having been vastly overrated. No anchorage near the shore which is accessible even by boats, only at high water; and of fresh water there is a general scarcity. The land is very good in patches, well calculated for a few settlers, but by no means adapted for a government settlement of any importance. Snakes are very plentiful. Two pigs, which were bitten, died in a few minutes. One of the privates of the buffs was also bitten; but, notwithstanding very alarming symptoms, he has entirely recovered, by the very skilful treatment of Mr. Henry White, the surgeon, attending the expedition.
Henry White's health suffered and when the Westernport settlement was abandoned he was sent to Port Stephens to be assigned to the Australian Agricultural Company.
He was at Port Stephens in the years 1830 - 1832 and referred to by Company Commissioner Sir Edward Parry as 'troublesome'. In February 1832 he was transferred to Mr. Cox in Maitland, possibly in exchange for William Whitelaw, and later that year returned to Port Stephens.
His sentence ended in October 1832 and he entered private practice, settling eventually at Windsor. In giving evidence in a court case in 1838 he described himself to have formerly been an assistant surgeon in the army. 
He married Mary Ann Townshend in November 1842. He is said to have fought a duel with an army captain around this time.
He discovered rich load of copper in March 1845. ....Discovery of an Extensive Lode of Copper Ore. - An accidental discovery of this precious metal was made some time ago by our venerated townsman Dr. Henry White, next to the estate of Mr. William Bowman, in the district of Wellington. Samples of the ore were sent to the Colonial Secretary, who forwarded them to England, where their properties were tested, and proved to be the most profitable description of copper. The beds of ore are supposed to extend for miles in every direction from whence the discovery was made; and a high hill in that neighbourhood presents indications of being a solid mass of treasure. - Hawkesbury Courier.