We don't. In fact, if Eliza is a legitimate Abbott or an illegitimate Eliza Neal, she almost certainly did die in infancy. I have been unable to find an Eliza Abbott or Eliza Neal of the right age and birthplace in the 1841 or 1851 census. A third option - that she is an unregistered illegitimate child of another surname who did not die in infancy - is a dead end as far as investigation is concerned, unless sometime in the future the civil death register is re-indexed to allow searches on the father's name.
There are two Eliza Neals in the census born about 1840 in London, but both have married parents. I found the baptism of the daughter of John and Elizabeth in Whitechapel in 1841 (born 21 Sep), and the daughter of William and Jane was born 1839/40 in Brompton.
I have found a couple of Eliza Neals buried as infants 1840/41. One that just might be relevant is Eliza Ann Neal, buried on 30 May 1840 at Christ Church Spitalfields, aged 9 weeks, residence Blossom Street. There is no Eliza Ann Neal(e) birth or death in the civil register - just the Eliza Neal death registered Jun qtr 1840 at Whitechapel. Exactly 9 weeks gives a birth date of 28/29 March, so she could only be Eliza Abbott if the minister or parent(s) have got the month wrong at her baptism; or (less likely) the burying minister has written 9 in error for 4.