Just a bit of extra info to help in your search. From another shipping list for the Rose found by JM arriving in 1855, parents' names are John and Mary.
I wonder if your Daniel and Rose did arrive separately, and didn't actually marry because one of them was already married. I see a marriage in 1855 for a Rosa GAFFNEY to Young RAITANG (bit of a weird name) at Dungog (FamilySearch), but no follow up family. This might be the one mentioned above.
There is also a family arriving in Dec 1841 on the
Lalla Rookh - James McGUIRE and his wife Rose. This Rose was also a GAFFNEY, parents James and Bridget from County Cavan. This Rose was born around 1814, and they had two children with them, Catherine (2), and Bridget (3 months), with another two born after arrival. This is too old for your Rose, but I am giving it to you in case you come across mention of this family and you will know to discount them.
The 1859 birth cert details for Mary KINNAR should give her mother's maiden name and at least tell you if you are on the right track or not. Do you have an occupation for Daniel?
Debra
