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I realise this is an old thread, but I've just come across one possibility for Mary Quinn that others might also like to research.  Mary's death certificate said she died in 1860 at the age of 34, that she was born in Dublin and had been in Australia for 30 years. 

An Eleanor Quan was transported from Tipperary in 1836.  With her on board was a 41/2 yr old female child.  I haven't been able yet to establish the child's first name, but so far it's the closest I've come to finding a child near the right age.  It would, however, mean that if this was Mary, she had her first child John at the age of about 13. 

Amusingly, Eleanor is described as having a cast in her right eye - my sister and I both have this problem, but of course this proves nothing.