Rebecca Smith
born 21 August–20 September 1833
  in Warton, Lancashire
died very roughly 1903

This baptismal record looks very much like the right girl (only problem being that it's 26 miles from Preston):
Baptisms: 22 Sep 1833 St Oswald, Warton Nr Lancaster, Lancashire, England
  Abode: Yealand
  Occupation: flax dresser
  Baptised by: Jas BARNS
  Register: Baptisms 1813 - 1840, Page 147, Entry 1173
  Source: LDS Film 1849662

1836: Harry Jack says that Grace Smith's baptism record in the online Parish Records shows the family living in Spring Street, Preston—a continuation of Bow Lane.

1838: Harry Jack says that young Joseph's baptism record shows the family living in Marsh Lane, Preston—Spring St/Bow Lane joined it.

1841 census: living with mother and siblings, and ?lodgers at ?Brigs Lane, Preston. Age is 6, born in county.

NB date of birth is based on her being older than brother Alexander, who was christened in December 1834.