You can check out St. Cuthbert's parish in Edinburgh. There atXXXXXin the 1841 census were living:
XXXXX XXXXX 48 M b abt 1792
XXXXX XXXXX (probably Mary Elizabeth) 35 F b abt 1806
XXXXX XXXXX 10 M b abt 1831
Charlotte Stewart 8 F b abt 1933
Georgina Stewart 5 F b abt 1835
XXXXX XXXXX 1 year 6 months M b abt 1838
This is the only family that comes close to resembling Georgina Ann, Georgiana, etc.
Civil registration of births did not begin until 1855 in Scotland, so you will need to check the old parish records. Some have been indexed, but searching is something you will need to do in person or hire a local genealogist in Edinburgh to do for you. You can read more below:
St. Cuthbert's, Edinburgh, Midlothian is Old Parish Register (OPR) 685.