Is there any independent source for her year of birth apart from her own claimed age? The reason I ask is that a child in an English orphanage would definitely be recorded in the 1901 census and here she is:
"England and Wales Census, 1901," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:X9XZ-4F3 : accessed 20 May 2016), Agnes O Leary, Croydon, Surrey, England; from "1901 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing Croydon subdistrict, PRO RG 13, The National Archives, Kew, Surrey
but there's a big problem with this record - she's 13, indicating a birth year of 1888 (assuming she kept the same birthday). The institution is the Virgo Fidelis Orphanage, Central Hill, Upper Norwood http://www.childrenscottagehomes.org.uk/virgo_fidelis_orphanage_upper_norwood.html
The name's correct, she's born in Ireland, and it's a Roman Catholic orphanage. If it is her then I can only suggest she used the opportunity of emigrating to knock a few years off her age. What about Hereford? My guess would be this one: http://www.childrenshomes.org.uk/HerefordStVincent/ You can email the archivist and she has admissions from 1892 so it's possible Agnes is listed. It seems to have been for younger children so perhaps she transferred to the Upper Norwood orphanage aged 11 or 12.