You have time to still get a passport for her, which is what I would recommend for all travel. It covers all the identification bases.
In addition, yes, you and your husband, who have sole custody, should write a letter of authorization to the adult in charge, providing travel dates, your personal contact information in case of an emergency, insurance information, etc.
And Yes, do include copies of your insurance and passports. We travel a lot and separately quite often, but with our biological children, and having a passport and letter of authorization answers all questions. I have one time forgotten the letter and it was indeed a huge hassle and consumption of time as the crossing guards at the Canadian border took the time to call my husband to ensure I was not abducting the kids. Remember, it's their job to scrutinize travelers. Don't fib about age the poster below recommends. Ugh....that's terrible advice.
PM if you want the letter I write up, otherwise, juggle google travel authorization letters and you'll find templates you can down load and edit.
And blessings on you for taking in a needy soul!