www.freebmd.org.uk indicates that Anna Maria died in the 4th quarter of 1854 at Bethnal Green, London. She does not appear in the 1851 census.
An application for a death certificate might help you. If would give the date of birth if known. It would also name the person who reported the death. If Anna died as a child the informer might well be a parent.
You don't say if you have other info related to your enquiry so I hope this helps.
There was no birth registration in 1856 but there was a second birth registered in Bethnal Green, Sep.1855, 1c, 220. A copy of that certificate will give details of the parents. I cannot see Anna Maria Quatermass on any census but there is a marriage under that name in the West Ham district Sep.1885, 4a, 184, her probable partner being an Alfred Irwin. on the 1891 census there is an Alfred Irwin with wife Anna (or Anny) M and 3 children at 4 Alderney Road, Mile End.