It is unusual for a statutory rape charge to be pursued under the circumstances you describe, unless somebody makes it an issue.

The hospital and doctors will be there to provide the mother with care, not to try to calculate how old the father may have been at the time of conception (or even, for that matter, if conception occurred in Florida or in some other state with a lower age of consent).

With the consent of the father's parents, or if they wait a month until he is an adult, there should not be any problem getting a marriage license.