While there aren't many Irish nicknames that specifically reference Irish girls, one that does is "Bridget." This nickname came about as a result of many Irish immigrants working as domestic servants.
Gender doesn't determine who gets which nicknames in Ireland. Instead, people get nicknames based on the criteria in which they fit. The nickname "Mick," for example, refers to an Irish person in general because many Irish last names begin with "Mac" or "Mc." "Paddy" is a derogatory nickname that references St. Patrick.
Another nickname for both males and females is "Cat-lick." This nickname came about because of a stereotyped Irish pronunciation of the word "Catholic." The nicknames "Turf Cutter" and "Bog-Jumper" refer to the bogs that were spread all over Ireland in the 1990s. The people who gathered these bogs to use for fuel for fires were called "Bog-Jumpers." The nickname "Turf Cutter" refers to an Irish groundskeeper.
The nickname "Fumblin' Dublin" is a name that Irish people give to unemployed Dublin residents. "McNugget" is a nickname that describes a child who is both Scottish and Irish. The Irish workers who help fill the Back Bay of Boston have earned the nickname "Muckers." Irish people use the nickname "WIC" to describe a white Irish Catholic.