I'm with George Churchill, and can find no record of anyone with a similar surname in NS records at that time. Findagrave does contain a lot of unsourced information and errors. We all struggle with this misinformation in one way or another. The trouble is figuring out what is right and what is the mistake.
In this case the gravestone doesn't indicate Elizabeth's maiden name or place of birth. She could have been born anywhere.
There is a Census that may show the same family in Nebraska: https://familysearch.org/ark:/61903/1:1:M8YP-48P
It doesn't give her maiden name either but it does show her DOB as 1824 in Canada. It occurs to me that Canada in 1824 referred to Ontario (Upper Canada) or Quebec (Lower Canada).Nova Scotia was not formally a part of Canada until 1867. So based on this information, I would search for an Elizabeth Augusta something, born around 1824 in Ontario or Quebec, who married George Young.
If she was born in Halifax, it was a port of entry for immigration, so and not necessarily a place everyone settled.
If you have a reason other than Findagrave to believe the Nitmore/Notmore was a valid clue, I wouldn't assume the English Naughtmire. She could also have been born of a German family such as Nuttmeyer. Even the Nitmore/Notmore might have been right - spelling was pretty fluid in those days, and we North Americans had a great deal of trouble getting German, Dutch, and other languages right.
Good luck with your searching!
