Hi bozzwell
I don't think you have the correct 1871 census, the one you mention is the wrong place of birth, is completely out of the area for the other censuses and she's with 2 others with the same surname who don't fit anywhere.
Having said that, I'm sure she is in service somewhere, but most probably not that far away from home.
The family didn't move far at all from 1851-1891.
Eliza's parents - Henry Head married Ann Anterton 18th August 1851 at St Pancras.
Dawn