Hi John,
I'm not sure whether you have found the shipping records yet but here they are from 
www.records.nsw.gov.au/archives/indexes_online_3357.asp#ImmigrationampShippi Assisted immigrants arriving in Sydney & Newcastle, 1844-59.
Surname Firstname  Age  Remarks    Vessel   Year   Reel    WILKES   Charles        31    and family    Kate     1854  2137, 2466   
WILKES   Edwin          1   
WILKES   Mary          35   
WILKES   Samuel         9      
WILKES   William          5   
PIGGIN   Eleanor        33   
The records may show age, occupation, place of birth, parents names, religion, whether they could read/write, if they had relatives in the 'Colony' and the fare.
I have been meaning to check a few other immigration records so I could check this too if you like. It may take me a week or two.
Believe it or not, I also have an interest in this family (although a very distant limb in my tree). Rose Wilkes (born 1886, G/daug of Charles) married Thomas Cheeseman in 1908. Thomas was a nephew of my GG G/mother.
Would you happen to have found the Charles & Mary in the 1851 Census? Are you in Aust ?  Happy to swap info.
Libby