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I wasn't even sure if the Irish registration method was the same as the English - hence the hope that someone could magically come up with her birth.
Will Father be traceable in 1911 just from his name and occupation?
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I think you would probably need to confirm the father's name anyway, especially since Doherty is such a common surname. Information on death certs is not always accurate, so you may need the additional clues.
There are not that many Mary Doherty (or variations) age under one year on the 1911 census and most have an age of a couple of months. Ages for very young children are not always transcribed but do appear on the actual form - they are usually rounded to the nearest month, but some say under 1 month. It's quite possible that knowing a father's name and occupation could narrow down your list quite considerably...
The Irish BMD indexes work in the same way as the English ones - you search a BMD Index on familysearch (instead of FreeBMD) which gives you name, year / quarter, registration distrct and register references... then you order potential certs from the GRO with these - see :
Introduction to Irish RecordsShane