Hi Julie,
I couldn't find any Peter Nairns born in Wigtonshire until 1852 and that's this one:
NAIRN, Peter
Gender: Male
Birth Date: 4 Apr 1852
Birthplace: Whithorn, Wigtown, Scotland
Recorded in: Whithorn, Wigtownshire, Scotland
Father: Alexander NAIRN
Mother: Jane GORDON
Source: FHL Film 1068042 Dates: 1789 - 1855
I found the following two matching name and birth date, but not location?
NAIRN, Peter Burgan
Gender: Male
Birth Date: 5 Nov 1815
Christening Date: 29 Nov 1815
Recorded in: Coldingham, Berwickshire, Scotland
Father: James NAIRN
Father's Father: Peter NAIRN
Mother: Margaret ROBERTSON
Mother's Father: James ROBERTSON
Source: FHL Film 1067869 Dates: 1727 - 1819
Note: Additional Data in Original Record
NAIRN, Peter
Gender: Male
Birth Date: 2 Feb 1815
Birthplace: Dunfermline, Fife, Scotland
Recorded in: Dunfermline, Fifeshire, Scotland
Father: James NAIRN
Mother: Mary BURT
Source: FHL Film 1040104 Dates: 1797 - 1820
The above info was taken from the British Vital Records.
If you'd like any more info, e.g. siblings of any of the above, just let me know.
Anne