David, I'm not sure which ancestor you are enquiring about?
Brian Lawson's index of registered births has:
Thomas Arthur GOLDSMITH [born] 20 Feb 1893 And[reas], [father] Walter GOLDSMITH [mother] Rohda DAVIS.

Other children's births:
Eliza Isabel GOLDSMITH 4 Aug 1888 And Walter GOLDSMITH Rhoda DAVIS
Henry Walter GOLDSMITH 19 Sep 1890 And Walter GOLDSMITH Roda DAVIS
Laurance Ed GOLDSMITH 27 Jan 1896 And Walter GOLDSMITH Rohda DAVIS
Margaret GOLDSMITH 19 Jul 1900 And Walter GOLDSMITH Rhoda DAVIS
Robert Percy GOLDSMITH 24 Sep 1898 And Walter GOLDSMITH Rhoda DAVIES

BL's marriage index has:
GOLDSMITH, Walter [married] 17 Feb 1888, District: R, Vol: and[reas] Page:17 [to] DAVIES, Rhoda.

If you meant records of Thomas Arthur in Australia (your ancestor's brother) his WW1 service record is freely available online: Title Goldsmith Thomas Arthur : SERN 4127 : POB Ramsey Isle of Man : POE Liverpool NSW : NOK W Goldsmith Emily. 33 pages. At: recordsearch.naa.gov.au/scripts/Imagine.asp?B=4770710
[He wrote that he was born in the parish of Andreas, near the town of Ramsey.]

His next of kin was wife Emily with an address in Kirk Michael IOM - Ballacorlett Barregarrow? Her previous address is crossed-out, and there is an unreadable date (1934?). The changes are in red "medical sheet held".
He enlisted in Liverpool, NSW, 11 Jan 1916.
He spent a lot of time in and out of hospital, and was in London in 1919, and granted leave with pay from June to August 1919 "Reason: Farming" by Attending: J Dugdale, Andreas Village Isle of Man. He returned to Australia in October that year.
The Queensland branch of the Repatriation Dept applied for repatriation benefits on his behalf in 1963.
There is a copy of a letter from him requesting his war medals dated March 12th 1928, with the address c/- Mr E Wolter, Byers St., Newstead, Brisbane. In this letter he says he was discharged in Sydney 27th Jan.1920. Discharge No.R86447 Reg No.4127 14th Light Horse Reg.
I'll leave you to go through the other 20 pages.
The Queensland deaths index is online only to 1964.

Craig Garrett wrote on the BB last year (3 March 2009) "I have an Emily Norton who married Thomas Arthur Goldsmith in my family tree. They married on the 29 April 1912 at Peel. Emily Norton was the daughter of John William and Sarah Norton living at Barregarrow, Michael in the 1901 IOM census.
Emily was Thomas Arthur Goldsmith's first wife. His second marriage was to Isabella Wade.... " etc.), and left an email address.

Sue