In the 1841 census for Grasmere, there is a Jane Hayes, aged four years, in a household with John Dixon aged thirteen and Isaac Pattison, aged 28, a stone waller. All three were born in county.
Jane was mis-transcribed as Jane Hayer.
I don't know if this is your Jane but do either of these two surnames fit in with what you know about your ancestors?
I can see no sign of either John or Mary Hayes on this census.
Cheers,
Jen