Why don't girls cover their head when davening?
This is a really simple question which does not have a simple answer.
The Shulchan Aruch (סי' צ"א סע' ג) paskens that it is אסור to say a Beracha without a head covering. The Shulchan Aruch is based on 1 opinion in מסכת סופרים which Rabenu Yerucham paskens like l'halacha. The Mishna Berura (סי' ב' ס"ק י"ב) paskens like the shulchan aruch.
By issurim, there is no distinction between men and women, issurim apply to both equally. Therefore, this issur of not saying berachos without a head covering should apply to women as well. We don't find any source to distinguish here between men and women.
In fact, the sefer ישכיל עבדי draws exactly this conclusion. He quotes the shulchan aruch and says he doesn't understand how the Beis Yakov's allows the girls to daven without covering their heads.
R' Ovadya Yosef has a teshuva about this (יביע אומר ח' ו' סי' ט"ו). He has a long discussion about whether it is an issur to say a beracha bareheaded or just a מדת חסידות. He brings rishonim and acharonim on both sides and concludes that the minhag today must be to rely on those who hold there is no issur. However, he recommends that for Shemoneh Esrei and Bentching that girls should cover their head to be חושש for the shulchan aruch.
It is absolutely fascinating how this din is completely ignored by the חרדים לדבר ה. After all, the Shulchan Aruch and Mishna Berura both pasken that it is assur, why are we not at least חושש for their opinion? The Charedi world has adopted so many wilder chumras why is this one left behind? There is no question that this chumra has much more basis then disallowing certain color stockings.