I agree Edgar seemed a good bet for her father BUT an Alice Dutton aged 3 died in Dec.qtr.1854 Birmingham which I think is probably Edgar's daughter. (Edgar a widower in 1861, no Alice with him, wife died 1852 and he remarried to a Jane Mary Box in 1862 and no Alice with them in 1871). The other Alice (b.1850 mmn Stone) I think could be the one who died Jun.qtr.1858 Birmingham aged 8.
Definitely something weird going on here. Absence on 1881 census, no marriage, no birth entry for dau. Jane Maria. No sign of Alice with surname Dutton in 1861 or 1871, no sign as Moss in 1881.
Annette