Had a look at the 1841 and 1851 censuses looking for a family consisting Henry, Mary & child Elizabeth b. abt. 1837.
In 1841 the only close one I can find is in Exminster - Henry & Mary, a child Mary, age 4 and a child Eliza age 1.
In 1851 they're still in Exminster Henry, 37, ag lab, b. Exminster, Mary, 35, Winkleigh, Eliza, 11, Exeter, Henry 9, Exminster, Elizabeth 6, Exminster, Jane, 3, Exminster, Thomas 10m, Exminster.
They are possibly the Henry Davy & Mary Beer who marry in nearby Alphington 6 nov 1836 according to the IGI.
Exminster is just outside Exeter.
I don't think that's your family ... but thought you should see it.
I can't obviously find another Henry & Mary Davy/Davey together in Devon in 1841.
In 1851 there are 2 appropriately aged Elizabeth Davy's b. Plymouth living with grandparents in Plymouth.
One is age 12 living with her widowed grandmother, Ann Davey in Plymouth.
Second is age 11 living with her grandparents William & Eliza Sadler(?) also in Plymouth.
Finally in 1851 & perhaps most interestingly there is an Elizabeth E Davy age 10, living in Stoke Damerel, b. Plymouth, living with her mother Mary Ann Davy & siblings, Frederick, Mary Ann & Edwin. It's hard to tell if Mary Ann, who is listed as a carpenter's wife is M or W - the enumerators M & W look almost identical to me! I can't spot an obvious Henry alone in Devon who is a carpenter.
Is the information you have from marriage certificate - or death certificate - or do you have both?
Sorry all this isn't more conclusive - but I thought you may be interested to see what there was, however unhelpful!
good luck
louise