you cant filter by parishes on the main 'all-Ireland' search page - you have to go to the county section to do that. There is usually a little icon, I think it's a magnifying glass to the right of the record detail, that jump to the county section when you click it. Once you are in the County section you will see a drop-down list to allow you select a parish to search.
If Anne was RC and was born in Buncrana, it looks like there will be no records for her family, since they only go back to 1864 for that parish. I suspect the record you found is located somewhere else - although it could be an adjoining parish.
There's a map of Donegal RC parish on the Irish Times website - see
Donegal RC Parish MapShane
