Just to help us see what is possibly known already:
1841 Cliff St, Ramsgate
Thomas BURGESS 50 grocer not born in Kent
Ann 40 not born in Kent
Charles 10 not born in Kent
Alfred 8 not born in Kent (baptised Bethnal Green)
Joseph 5 not born in Kent (baptised Bethnal Green)
Elizabeth 3 not born in Kent (baptised Bethnal Green)
James 4m born in Kent (baptised Ramsgate)
HO107/469 book 6 folio 51 page 22
Possibly also Albert baptised 1843 Whitechapel?
It doesn't look as though they were in Ramsgate for very long.
Have you actually found them in Australia and, if so, where?
A birth certificate for James would give his the maiden name of his mother but there are two to choose from
Casalguidi