Your case has two parts. First, terminating the rights of the biological father. It is cheaper if he agrees and signs the proper documents. The court will first have to terminate his rights before it gives parental rights to your fiancee. It is imperative that you use the correct forms and not just some forms you find on the internet. Every state has slightly different requirements and forms that birth parents must sign to consent to an adoption. Some very good adoption attorneys in St Louis.
The second part of your case is giving legal rights as a parent to your fiancee. Simply stated, the court will only do that if you are married. There may be an exception or two, but those are rare cases.
Depending on your state law, the attorney may be able to obtain the biofather's consent and hold it until after you are married. Remember - this is an issue of state law and only a Missouri attorney can answer that question.
While the birth father is signing the consent or surrender, your attorney should also ask him to complete a thorough Family, Medical & Social History. That is the best gift he can give to your daughter. Having medical history is so important as we go through life.