My first thought is [name_f]Bonnie[/name_f]. Though uncommon in the British Isles, I can see a little redheaded girl named [name_f]Bonnie[/name_f].
A few other ideas:
[name_f]Isabel[/name_f]
[name_f]Nora[/name_f]
[name_f]Imogen[/name_f]
[name_f]Paloma[/name_f]
[name_f]Tallulah[/name_f]
[name_f]Charlotte[/name_f]
[name_f]Rose[/name_f] nn [name_f]Rosie[/name_f]
[name_f]Louise[/name_f] nn [name_f]Lulu[/name_f]
You should pick an Irish name that was common in that period, but also something her parents would pick based on personality. [name_f]Do[/name_f] they pick based on memories or personal experiences, meaning, or the way it rolls off the tongue? Are they actually from [name_f]Ireland[/name_f], living there, or some other country? If she’s an Irishmen from [name_f]Ireland[/name_f], then I have a few Irish names:
[name_f]Elspeth[/name_f] nn [name_f]Elsie[/name_f]
[name_f]Katherine[/name_f] nn [name_f]Kitty[/name_f]
[name_u]November[/name_u] nn Novi
[name_f]September[/name_f] nn [name_f]Emmi[/name_f]
[name_f]Emmeline[/name_f] nn [name_f]Emmi[/name_f]
[name_u]Rowan[/name_u]