Not sure if this is your Annie, but there was an Ann Howell born Sept 15, 1858 in Carbonear to Albert and Lavinia (nee Cox) Howell. Albert and Lavinia married on Dec. 18, 1856.
Other children of record for Albert and Lavinia were:
William b. July 2, 1862
Arthur b. Aug 20, 1865
Sophia b. Aug 7, 1869
My observation is that Howell surname had a strong early presence in Carbonear; there is a good possibility your Annie could have been born here.
Having said that, there is an Elizabeth Ann Howell born in Hant's Harbour on Sept 25, 1852 to Francis and Grace Howell. However, she seems to be not quite lined up from a birth date perspective.
I did see her daughter Emily Merchant's baptism record as well; she was born Dec 29, 1875 in Hant's Harbour to William and Ann Merchant; I did not see any records for the other children. Given your Annie's age, that would have had to be their first child.
Hope this info (although inconclusive) is of assistance.
Carol