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I checked Roots Ireland and there were no baptismal records in Galway East for children of James Murphy and a wife with the surname Carr. Records for Ahascragh/Killosolan/Caltra parish start in 1840 so it is likely that Ann was also born pre-1840. You can look at the register to see if you can find any records.http://registers.nli.ie/parishes/0535
I also looked at the 1855 Griffiths Valuation for Co. Galway. There are two civil parishes: Ahascragh and Killosolan which correspond to Ahascragh/Killosolam/Caltra RC parish. There were no James Murphy records in either parish.
Questions? Have you considered autosomal DNA testing?