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Is there any chance that you could get their marriage certificate as if that gives her father's name it might make it easier to find her birth here?

Iv'e learned from my uncle that her fathers name was Martin, her mothers name was Mary and her twin sister was named Joan (maybe Joanna or something similar)

Trying to make sense of this 1841 Scotland census. To the best of my knowledge, my 4th gg Agnes Crawford married James Kilgour in 1834. They gave birth to my 3rd gg Agnes Kilgour and 2 other children between 1837 and 1843. Now this is where I get lost.

I found a 1851 Scotland census(transcription, not original doc) with the occupants as listed:
Samuel Nicol   30
Agnes Nicol   34
Bryce Nicol   1   (son)
Janet Kilgour   13 (stepdaughter)
Agnes Kilgour   11 (stepdaughter)
Jamesina A Kilgour   8 (stepdaughter)

So I went a decade back to try and find one with the two oldest children living with their father, and this is what I found in the 1841 Scotland census(transcription, not original doc):

James Kilgour   30
Agnes Kilgour   25
Jennet Kilgour   10 Mo
Margret Crawfert   25

My current theory, which totally could be wishful thinking, is that the ages/names have been mixed up in the transcription of the 1841 census. my 3rd gg Agnes Kilgour should be roughly 10mos, her older sister Janet would've been around 2.5 years, and my 4th gg Agnes Crawford and James Kilgour would've been 25 and 30. Even more convincing, is both the 1841 and 1851 census list George St, Ayrshire as their address. But without the original document, I'm unable to confirm where the name Margaret is coming from.. or if my theory is even remotely close. 

Are you sure about the 1st October, that would come under the December quarter on the birth registrations and I can't find any between 1930 and 1940 where two children had the same mother's maiden name.

My mom is pretty confident her birthday was Oct 1, as it was also the date I was supposed to be born. But something could be muffling her memory. Im pretty sure she passed away around 2003/2004, I know that I was in elementary school. I can't even find an obit or death record though which is making it incredibly hard to confirm dates.

I'm not sure of her twin sisters name, and she definitely survived. My mom remembers her going by a shortened name like my nana did.