First name sometimes recorded as Beniah.

In October 1845 at Starks, Maine, he married Apphia Higgins Collins; they had two daughters. All four Bradfords are recorded together in the same household in the 1850 U.S. federal census in Starks.

He does not appear in any later U.S. censuses, by himself or with Apphia. In the 1880 census she is recorded as a widow, re-marrying in 1894 to Zaccheus A. Dyer. Benaiah reportedly married an Ellen O'Donoghue around 1877 in Bowen, Queensland.

Benaiah arrived at Melbourne in August 1853 from New York, via Rio de Janeiro. A "list of passengers from Maine -- nearly one hundred in number, and mostly from Somerset County -- sailed in the ship Rockland for Australia a week or two ago." The list, in the 12 May 1853 Eastern Mail (Waterville, Me.), p. 4, col. 2., gives hometowns, and includes a B. P. Bradford of Starks. [available from Colby College at http://digitalcommons.colby.edu/eastern_mail/302/]
His name (Bradford, Benaiah P.) is given in a list of unclaimed letters at the Melbourne General Post Office published in the 30 December 1854 Argus (Melbourne, Vic.), p. 6, col. 2.

Behaiah apparently began working at goldfields in Victoria, the next large gold discovery after that in New South Wales. A January 1855 news article in The Argus places him in central Victoria, where he had been robbed, but recovered his belongings. Some two decades later he lived near Cooktown, Queensland, a seaport municipality named for Captain James Cook, over two thousand miles north of his original arrival point, Melbourne. Bradford was likely drawn to the Cooktown area by the 1873 discovery of the Palmer Goldfield and the governmental decision to develop Cooktown to service the goldfield. He had the license of the Diggers’ Rest Hotel at Four-Mile Camp outside Cooktown from 1874 to 1887, and then in 1888-1889 managed the Shamrock Hotel in town. In 1891 he owned a block of land with two cottages in Cooktown, living in one and renting the other. Benaiah was still residing in the town in 1900, and died in Queensland that year.

The Australia Death Index, 1787-1985, at Ancestry gives the death registration place as Queensland, registration number of 001081, and page number as 2559.

The Australia Cemetery index at Ancestry.com, based upon the Cooktown Cemetery register, lists his first name as Beniaga [sic], age 84, Church of England, Publican, buried 1 October 1900.