Hi Carol,
I've been doing a little bit more digging and thanks to a previous post by Jennifer Porter I have cast my search a bit further afield.
A google search for Arabella Dora STONEHOUSE turned up a marriage in 'The Empire' newspaper' in Sydney, dated Saturday, October 24, 1874. Transcript as follows:
"Woollahra.
On September 26, at Trinity Church, Glen Innes, by the Rev. G. M. Johnson, H.A.,
William, son of William Henry Archer of Brooklyn, New York, U.S.,
to Arabella Dora, daughter of Matthew Charles and Elizabeth Stonehouse, of
Lithe, near Whitby, Yorkshire, England."
The newspaper can be found on the TROVE website - the Australian equivalent of the BNA.
I hope this helps in your search.
Find a grave also have mention of her burial in Rookwood Cemetery.
Kind regards
Joan