Where did Dromore come from? Is it from a census?
Assuming that this comes from a reliable source, the first thing is to establish which parish Dromore is in. The Gazetteer of British Place Names puts it in the civil parish of Kirkcudbright, so if Sara was born in Dromore one would expect her birth to have been registered in the parish of Kirkcudbright.
There is only one Sara(h) M(a)cmillan registered in the parish of Kirkcudbright before 1900, but she was born in 1894, which is a bit late to be your one.
So could she have been illegitimate and registered under a different surname? There are 20 births of Sara(h)s in the parish of Kirkcudbright between 1875 and 1890, of whom 11 of their mothers' maiden surnames are not in the births index, which may imply that they were illegitimate, or it may just mean that the mothers' surname have yet to be added to the index.
You could make a note of those 11 Sarahs' surnames, and try to eliminate any you can find in the first census after their birth, and then look at the original birth certificates to see if any of them were born on 24 November.