She could have been a servant in another household in the 1841 and 1851 censuses (in Liverpool in 1851). The burial in 1858 might have an address.

Donna, is there anything more in the Patrick burial record for:
MOORE, Margaret 35 Patrick 8 Sep 1858 - or even a M.I.?
Also parents Thomas MOORE (possibly buried Patrick 10 Jun 1869) & Ann [Shimmin]. Very many thanks for looking!

Sue