My understanding is that they were buried at sea, as there would have been no means of preserving bodies. People were examined by doctors prior to embarkation in order to reduce the risk of epidemics, but even so, diseases such as scarlet fever decimated some ships. There were no antibiotics, conditions would have been crowded and the transmission of disease was not well understood. Food was not always the best for those in steerage, so diarrhoea was often a problem, especially amongst young children. Bodies were often buried within hours of death, sometimes with only the parents present. I have heard that in seas where sharks were prevalent, such burials generally took place prior to day break to minimize potential distress of relatives. Migration wasn't without its hazards! You may be interested in a book about life on the migrant ships, "Over the Mountains of the Sea", by David Hastings, published 2006 by Auckland University Press.
Using the name "Indian Queen" a search of the NZ database of old newspapers, PapersPast, produced an article with log details of that particular voyage of the Indian Queen. See Daily Southern Cross, 17 February 1857 at http://paperspast.natlib.govt.nz
You will find other news items in the same database regarding the "Indian Queen" - apparently many passengers travelled on promisory notes that they would be employed as soon as they arrived - this money being used to repay their fares. These promises were not necessarily honoured. I have found one reference in the Petone Settlers' Museum database which states all 405 passengers were "assisted" immigrants.
There are also about 100 references to "Ollerenshaw" in the PapersPast database.