You don’t need a certificate of citizenship to get her her passport (or at all, many people forego the expense and just get their kids a passport). You could have applied /can apply at the same time as you did for your passport with pretty much the same information you did - that’s all you need, plus her birth certificate. I suggest you do so now with an expedited application.
From the passport form instructions:
Claiming Citizenship through Naturalization of One or Both Parent(s), submit all the following:
o Your parent(s) Certificate(s) of Naturalization (you have… unless you already sent it in for your own passport application?)
o Your parents' marriage/certificate and/or evidence that you were in the legal and physical custody of your U.S. citizen parent, if applicable (if parents not married something from school, doctor etc showing same address as you is fine)
o Your foreign birth certificate (and official translation if the document is not in English)
o Your evidence of admission to the United States for legal permanent residence and proof you subsequently resided in the United States (her green card)