I do not practice in DE, but I may offer some general advice. First, you mention asking for permission to marry. Are you on probation? If so, you should ask your probation officer these questions. Probation officers generally have some level of control over whether you may marry.
Second, you can ask your probation officer to make an exception related to your fiancee's child. But ultimately, you may have to ask the court to allow you contact with your fiancee's child. This way, you could marry and live together immediately.
If your probation officer does not object, there is likely no reason you cannot marry and live separately for a time.
Bear in mind if your fiancee's daughter's father is actively involved in the daughter's life, the father may object to your being around the daughter. If so, the father could move a family court to take action (i.e., prohibit you from contact with the daughter, prevent you from living with fiancee, ask for sole custody and placement of daughter, etc.)
Sign up to receive a 3-part series of useful information and advice about child custody law.