burial register can be bought via soc, they are on Mormon microfilm or possibly SKS will look for you - however if the bodies not found no burial ! - you are however post 1877 so there will probably be a death cert (however Kelly !!)
I thought I gave you the 1881 census - the entry from the home lists an elder sister - are we know talking about the same person ?
BTW there are 6 Sarah Kellys aged less than 6 years in 1881 (1 lives in 8 Chester St Douglas another poor area) - however none appaers to fit pattern of mariner father