Just for a thesis. It's rumored her father is
James Samuel Doak
Born: Abt 1670 - Ballymena, Antrim, Ulster, Ireland
Died: Abt 1753 - Donegal, Chester, Pennsylvania
I cringe at the source which is extremely derivative - Edmund West (Anyone with access to ancestry is familiar) See G2G-215437
I however did find a Sar Record (Sons of the American Revolution Membership Applications) SAR Membership: 35566 for the son Alexander Breckenridge which alleges Ann Doak to be born in Ireland however it doesn't say specifically where in Ireland
George Breckenridge who appears to have not emigrated till about 1740 according to the U.S. and Canada, Passenger and Immigration Lists Index, 1500s-1900s Philadelphia, Pennsylvania; Year: 1740; Page Number: 52 See Ancestry Link
Now I have found nothing that says when James Samuel Doak the purported father for Ann Doak emigrated
The whole record appears to need a fine toothed comb and someone whose mind isn't 100 different places.