Don't know if this might be the same Elizabeth Quantick
Eliza QUANTIC single 28 born Ashcombe Devon Occupation Nursery Maid
Cowley More, Tiverton, Devon - Head Lucy Short
1851c HO107 1889 Folio 38 Page 1
Perhaps not as there's also an Eliza Quantic on 1841 census
Mamhead Cottage, Mamhead, St Thomas, Devon
Eliza QUANTIC Age 15
others same household
Agnes, Henry, Sarah, Thos, Mary, Willm last names Michelmore, Waydon, Mosey, Walters
HO107 Piece 220 Folio 6 Page 7
The above could indeed very easily be Elizabeth QUANTICK the daughter of Thomas and Eleanor, though? The 1841 Census with the Michelmore family, she is a F.S. (Female servant in the household).
And as you say, Elizabeth QUANTICK the daughter of Thomas and Eleanor - is not in her father's household in 1841. Nor is she with him 1851. Nor with him in 1861. I followed that family a bit, partly looking for marriages of siblings to see witness names (hoping for an Elizabeth

but no luck ). Here's what I jotted down anyway - you may have all/some of this, so for reference:
MARRIAGE 1819:
Thomas Quantick married Eleanor Rugg, 19 Oct 1819, Mamhead
CENSUS 1841: Ashcombe
Piece 219- Book 1- Folio 6- P 7
Thomas QUANTIC, 50, Ag Lab, with (in order of listing:)
Mary 20, Ellen 8, George 8, Harriet 6, Andrew 1
CENSUS 1851: Ashcombe
HO107- Piece 1867- Folio 663 -P 3
Thomas QUANTIC,
40, widower, Farm Labourer
(Thomas' age is way out - he is about 62 here)Dau: Ellen 18, unm
Son: Andrew 11,
And next door:Head: Henry QUANTIC 36, Farm Labourer
Wife: Jane 35
Dau: Ann 13
Son: Elias 10
Son: Joseph 6
Visitor: Eliza'th KENTSBEAR? 23, Serv't, b Crepiton
MARRIAGE 1851: At Ashcombe
On 31 Dec, Ellen Quantic, dau of Thomas Quantick, of Ashcombe, married George Gilpin.
Witness: James Quantick, Harriet Bolt.
CENSUS 1861: Ashcombe, Labourers Cottage:
RG 9; Piece: 1392; Folio: 150; Page: 2;
Head: George GILPIN 30, ag lab
Wife: Ellen 28,
Children: James 9, George 8, Miriam 6, Henry 4, Fred'k 10mth,
Father: Thomas QUANTICK 72, Widower, Ag Lab
DEATH 1865: Thomas QUANTICK age 76 years, Abode: Ashcombe
Buried Ashcombe, 10th October 1865.
Cheers
AMBLY