There is no way to know. If the child's father will consent to the adoption, it can be a relatively quick and easy process. If he does not consent, it can be a very long and difficult process. Only you can guess whether the father will have a problem with an adoption.
Yes, it is possible for your fiancé to adopt your daughter; this can be done either before, or after you marry, although being married to each other is preferable. With regard to the biological father, if he is willing to consent to the adoption, there should not be a problem. If the father is not willing to consent, then you either need to decide whether adoption is a viable plan or not. It would be best if you consult with any attorney who is well versed in adoption law and procedure to determine your best course of action. I have changed the practice area of your question to 'adoption', Many attorneys, including me, offer a free consultation on such matters.
Sara Howard is an attorney licensed to practice law in Illinois since 1983. Her practice concentrates primarily in adoption and family law as well as landlord tenant & real estate law. She is currently a member of the Chicago Bar Association's Adoption Law Committee, and a former bank attorney . Any response to a question on AVVO does not constitute an attorney client relationship, but is general information based on the limited information provided. Free initial consultations are offered.