The IGI has record of his baptism at Old Windsor on 26 Dec 1812, the son of James and Elizabeth Nibbs. He was baptised the same day as his brother John. It's the record of the baptism that links Joseph and John with this James and Elizabeth Knibbs who we know disappeard from Woodstock, Oxfordshire after 1800.
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The 1841 census shows Joseph, his wife and children, living at Bishopsgate Common in the parish of Egham, Surrey:
Joseph Knibbs 26 Ag Lab (born out of County)
Mary Knibbs 23 (born out of County)
Elizabeth Knibbs 7 (born in Surrey)
Joseph Knibbs 6 (born in Surrey)
John Knibbs 3 (born in Surrey)
James Knibbs 2 (born in Surrey)
Mary Knibbs 1 month (born in Surrey)

They were living in the household of John Lilly aged 60, and Anne Lilly aged 25.

We can see Mary as a widow in 1861 living at 119 Beford Street, Mile End Old Town, Tower Hamlets, Middlesex with her daughter Elizabeth and son Richard:
Mary Ann Knibbs Widow 45 laundress Bow Devonshire
Elizabeth Knibbs Daughter unmarried 25 Egham Surrey
Richard Knibbs Son scholar 14 London Middlesex
Sarah Foster Lodger 25 Needlewoman Hertford
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The 1871 census shows Mary Ann as a widow, living at Mile End Old Town, Tower Hamlets, Middlesex with supposedly, three daughters, a niece and a lodger:
Mary Ann Knibbs Widow 54 Lodging House Keeper Bow devonshire
Jemima Knibbs Daughter single 24 Machinist Egham Surrey
Sarah Knibbs Daughter single 28 Laundress Egham Surrey
Emily Knibbs Daughter single 8 Mile End Middlesex
Jemima Knibbs Niece single 4 Mile End Middlesex
Anna Farmer Lodger Widow 52 Silk Weaver Shoreditch Middlesex

We think that Emily is probably not the daughter of Mary Ann. Mary Ann's husband Joseph died several years before Emily was born. I suspect she is the daughter of Mary Ann's daughter Sarah.
We know that Elizabeth went off to live in America in 1871, and was joined there in about 1880 by an Emily Knibbs, aged 16, who is described at that time as her niece.

Jemima is probaly the daughter of Mary Ann's sister Frances Knibbs.
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In 1881 Mary is living with her daughter Mary and son-in-law at 3 Dante Rd., Newington, Surrey, England:
Richard PHILLIPS Head M Male 38 Whitechapel, Middlesex, England Fish Salesman Master Employing 2 Men
Mary A. PHILLIPS Wife M Female 40 Bishopsgate, Middlesex, England
Richard C. PHILLIPS Son Male 2 Newington, Surrey, England
Mary A. KNIBBS Mother W Female 64 Bow, Devon, England Income From Freeholds
Jemima KNIBBS Niece Female 14 Mile End, Middlesex, England No Occupation
Alfred SHARP Lodger W Male 62 Whitechapel, Middlesex, England Retired Oilman

The IGI has his parents as James and Elizabeth NIBB