I believe the title godparent does officially come from getting christened so there is no way to have her as a god parent on paper unless it’s a christening. You don’t need to be christened yourself to be a god parent. You can also unofficially name her a god parent but it won’t be on paper
I call my son's Fairy Godmother mostly because I'm not religious although I'm godmother to 3 children. I think it's fine to use the term as long you mean "an important and significant person in child's life who will love them".
My friend who's been there for us since day 1. She's called Aunty. My little girl has been christened. Buy my husband chose the godparents and they don't have anything to do with her 🤦♀️