Hi pollyfan,
I think you may have to get the Birth Cert to establish her Mothers name.
As a side, did you notice a Henry HADDON, born c 1862, Devonport, Devon, on the same 1871 Census as Jane?
If you look at the image it looks like Henry Staddon to me. A Brother?
1861 he may be Henry Staddon born c 1860 Pyworthy, Devon, a Boarder in Holsworthy.
1901 he may be William H Staddon born c 1859 Pyworthy
1881 William H Staddon born c 1862 Holsworthy, newly married to Annie.
Cant find a Marriage.
EDIT he may have married Annie WOODLEY Kilkhampton, Cornwall, 22 March 1881
Names his Father as JOHN, a Labourer (may have lied?)
Ann names her Father as John Woodley, CornwallOPC has a Baptism 1857 Stratton for her, Mother MARY JANE Woodley, Singlewoman.
So looks like she lied and is Illegitimate.
It fits as WH and Ann name their 1st Daug Mary Jane.