Hope it is ok to add my other brickwall to the forum

My great x 3 grandma is Harriet Bailey who married Amos Mason in 1869 at Etruria, Stoke. She names her father as Benjamin Bailey, Collier.
Harriet is born 1849c in Oldbury according to all census I have her on from 1871 to 1911.
I have so far been unable to trace her on the 51 and 61 census or a birth registration which would be in the right area. I HAVE found though on the 51 census in Oldbury a Harriet Smith aged 2 with parents Benjamin Bailey and Eliza Bailey. All the children listed have the surname Smith, except for a new baby which is down as N.K. Benjamin was listed as a Coal Miner which fits occupation on Harriet's marriage. (Class: HO107; Piece: 2024; Folio: 478; Page: 42; GSU roll: 87430).
I have found a married of an Eliza Smith to Bejamin Bailey in the June Quarter of 1849 in the district of West Bromwich which appears to cover Oldbury. There is also a birth registration in the June Quarter of 1849 of a Harriet Smith in the West Brom district.
Have I missed an obvious entry of a Harriet Bailey somewhere with a father Benjamin or does the the above sound like my lady?
Kind Regards
Claire