On familysearch there is a baptism of Mary Jane Witty d/o Richard and Phoebe on 3 Feb 1856 at Wellington, Staffordshire.
There is no corresponding birth in the Civil Registration Index, leaving the possiblity that this is your Mary Jane baptised not long before she died.
Familysearch also shows a marriage of Richard John WHITTY and Phoebe WRIGHT in Stoke on Trent in 1831.
Phoebe Witty wife of Richard John Witty is shown as a widow on the 1851 census so she can't be the mother of a Witty child born to Richard and Phoebe after 1851 (or 1852).
The reason it is hard to find her on the 1851 census is that she is listed as WILLY and has one child William with her. They are in the household of Phoebe's nephew, John Wright.:
Market Place, Burslem
John Knight, head, single, 18, butcher, employer, born Milton, Staffordshire
Phebe Willy [Witty], aunt, widow, 39, butchers housekeeper, born Bucknall, Staffordshire
Mary Knight, sister, single, 12, scholar, born Longport, Staffordshire
Edna Knight, sister, single, 8, scholar, born Burslem, Staffordshire
William Willy [Witty], cousin, single, 16, butchers assistant, born Bucknall, Staffordshire
Samuel Taylor, servant, single, 19, assistant butcher, born Burslem, Staffordshire
Ann Flanaghan, servant, single, 19, general servant, born Mayo, Ireland.
By the way, William Witty married his cousin Mary Knight in 1863. They emigrated to Australia in 1864.