Hi Richard,
There are 2 ladies in this family name Charlotte - one born in 1833 and one in 1861 but I guess you are looking for the earlier lady who married Thomas Perkins?
Her parents were James Brindley, born about 1788 in Nottingham UK and Mary Ann Searcey born about 1790 in Nottingham. James arrived in Sydney in 1826, co-incidentally on the same ship, the John Barry, and in the same Regiment of Royal Veterans as the above James Waller. James Brindley was posted to Tasmania but left there later for Sydney on the Sapphire on 26 February 1846 to seek work in NSW. He arrived in Sydney 7th March with 135 hired servants from Van Dieman's Land to work in NSW.
James died on 25th August 1847 at the Benevolent Asylum.
Hope this helps,
Shadrach