Who is considered a "legal peer" when marrying without a wali?

Selamu Aleykum, I have a question regarding the Hanafi ruling on a woman of "legal peerage" and marrying without a Wali. Currently, I am set to get married to a Christian woman, though I have not officially proposed because I have had immense trouble finding her wali/if she even has one. Her father unfortunately passed away a few years ago, and she has no brothers to speak of, being from an all-girls family. She barely knows any of the men on her father's side of the family, and of her mother's, both of the uncles she knows even remotely well she does not feel comfortable to represent her; and, as far as I understand it, a Wali must know the woman well enough to make a proper decision for her well-being. In trying to figure this out, whether an Islamic authority should preside as her Wali etc. I came to find the ruling in our Fiqh stating a woman of "legal peerage" could be married without the permission or presence of a guardian. I told her about this during conversation, and she said she was relieved because she "did not feel comfortable with anyone she knew other than her dad being her guardian, anyway." Knowing this, I've been searching for any other information to confirm if this is possible or not, as I want her to feel comfortable and accommodated. It seems in most legal respects she is my equal - ie of sound mind, adult, etc. but that is all I could find. I'm not sure if there is any information missing and - most crucially - I cannot find any information especially regarding her status of equality as a *kitabi* under the Shari'a for this purpose. So according to the ruling mentioned, is she considered my legal peer? Does it apply as well to Dhimmi or is it only applicable to a Muslimah, and are there any details I am missing? I am trying to do this right and make sure we are right in the eyes of Allah. Finally, if she is *not* my legal peer, who on earth can be her wali? Jazakhallah Khairun