The gemara says that when a ketana makes a shliach to receive her gett, it is not binding until the gett reaches her hand. Rashi explains that this is because there is no shlichus for a kattan, so the shliach she appointed to receive the gett becomes a shliach l'holacha and the gett is only binding after she receives it.
Why can a kattan not make a shliach?
Rashi 42a said because we learn shlichus from gett, and since by gett it says "ish", only a man can appoint a shliach not a child. Rashi in Baba Metzia 71a takes a similar approach, that another source for shlichus is teruma and by teruma we need someone who is capable of separating teruma, to the exclusion of a child who's hekdesh isn't binding. The Ketzos Hachoshen (188:3) asks: if we learn from teruma then a child who is 12 (mufla samuch l'ish) and his nedarim are binding, should be able to make a shliach. If we learn from gett, then a boy should not be able to appoint a shliach because it says "ish" by gett, but a girl should be able to appoint a shliach since she is capable of receiving her gett?
The Rambam (Gerushin 6:9) gives a technical reason for a girl not being able to make a shliach:
וקטנה אינה עושה שליח לקבלה אע"פ שחצרה קונה לה גיטה כגדולה, מפני ששליח קבלה צריך עדים ואין מעידין על הקטן שאינו בן דעת גמורה
The reason a ketana cannot make a shliach is that shliach l'kabala needs eidim to verify that they were appointed and it is impossible to have eidus testifying that a ketana had enough da'as necessary to appoint a shliach l'kabala. Meaning, although she has enough da'as to appoint a shliach l'kabala, she does not have enough da'as to convince the eidim that she has enough da'as to appoint a shliach l'kabala - the ketzos understands that this technicality can be used as a source as to why a girl can never appoint a shliach.