I didn't just outright ask her. She brought it up. She said she wants my fiance to be her "real" dad, and she wants the same last name as us. She asked if that could happen and I told her the only way was if she were adopted. I also explained to her that if that were to happen that her father would not legally be her father. I am also fine with her father still being a part of her life if she is adopted. It's a complicated situation. If he were to get control of his alcoholism I would be fine with unsupervised visits. Since he is ALWAYS under the influence of alcohol and sometimes also marijuana, I am not okay with him having her alone. He doesn't want to see her if he has to have a supervisor. So, she has barely seen him since we split up almost six years ago. We were never married. He wasn't even interested in going to court to become her legal father, he was bribed with money by his parents because they thought that would get them "grandparent" rights.
I feel like an adoption would be good for my daughter because my fiance is a responsible, well-educated man, and a very loving father. So, even if we WERE to get divorced (which I don't predict happening) down the road, my daughter would still have what she deserves-a loving father who doesn't let her down at every chance.
To answer other questions, her dad has joint legal custody, and I have sole physical custody, with him having supervised visits, as previously mentioned. He never sees her because he doesn't want to be supervised. He will not get help for his drinking so that he can have unsupervised visits.
Thanks to all who helped answer my questions. I really had no idea how this worked, or that we should wait a year, consult with a lawyer etc..