Hi Theresa,
At the time of the Griffiths Valuation for Co. Down (1863), there is no James McDermott living in Newtown townland in the parish of Kilbroney (Rostrevor). There is a John McDermott living in townland of Levallyclanone which is close but not that close to Newtown. Also, AncestryIreland has most of Kilbroney's baptismal records up on their (pay per view) website and there is no baptism there for Mary Jane (Kilbroney's baptismal records start in 1808 although the early records are patchy). However, there is a James McDermott living in the neighbouring parish of Kilkeel, located in the townland of Grange farming just over 8 acres of land (there is also a Clement and Patrick McDermott living close to James, so they may be brothers). There is also mention of a Clem and Brien McDermed living in Grange in 1803 who may be ancestors of the ones living in Grange in 1863. There are still McDermotts living in Grange in the 1901 and 1911 censes.
Mary Jane may have been working in Newtown as a domestic servant or living with relatives at the time of her marriage - marriage certs just give the place where they were living just before they married and not necessarily where they were born.
You would probably have a better chance of finding her baptismal record in the Kilkeel records which start in 1839 but are not legible until 1845. They are also microfilmed and can be accessed in PRONI in Belfast and the National Library in Dublin. if you cannot get to these places, you can order them from your nearest Mormon genealogical centre. After 1845, the Kilkeel records are transcribed and very easy to read but before that they are impossible! Kilkeel civil parish is divided into 2 religious parishes - Kilkeel and Mourne. As far as I know, Grange falls under Kilkeel religious parish but you could try Mourne if you have no success with the Kilkeel records. Sarah may have been born in 1844 so you might miss her baptismal record but she could have had siblings born after 1845 so you will probably find her parents there. McDermott was not a very common name for that area.
You won't be able to get a birth cert as civil registration only started in 1864 for births. I am surprised that you got her mother's name on the marriage cert as civil marriage certs only gives names of fathers and not mothers. Also, the Kilbroney marriage records (for that period anyway), only gave the names of the bride and groom and their witnesses. Did you get Sarah's name from the civil marriage record or from some other record?
Good luck with your research
Kind regards
Deirdre