I'm afraid you won't be able to get a birth certificate as such - registration of births, marriages and deaths didn't start in Scotland until 1855. Your best bet prior to that date is to look for baptism details in the OPRs (Old Parish Registers).

I can see two possibles in the IGI for Janet REID - assuming, of course, that she was from Little Dunkeld, and didn't come from a neighbouring parish:

JANNET REID
Birth: 23 FEB 1769
Christening: 26 FEB 1769 Little Dunkeld, Perth, Scotland
Father: JAMES REID
Mother: JANNET ROBERTSON

JANNET REID
Christening: 10 MAY 1772 Little Dunkeld, Perth, Scotland
Father: PETER REID
Mother: JANET REID

Not much to choose between them, alas...

Your other hope is that Janet died after 1855, as the death certificate gives full details of parents' names, etc. In this case, alas, I think it's probable that Janet died before 1855. :-(

Best wishes,

Sue