According to FreeCEN there is a two-year-old Eliza Norris in Edinburgh in 1841, born in Scotland but not in Edinburgh, in a household with what looks like her parents - John Norris, 25, born Ireland and Agnes Norris, 20, born Ireland, plus Robt Norris, 9.
There are six deaths of Eliza(beth) Norris, born 1833-1843, in the deaths index at Scotland's People. You could check these to see if one is the daughter of John Norris and Agnes. If so, then you can eliminate that one as yours.
It is quite possible that people could be recorded as Morris in one record and Norris in another, so your Eliza might turn up as Morris somewhere.