You and the child's father may fill out form DH-432 "Acknowledgement of Paternity." Both parents must fill out the form and sign it in the presence of two witnesses or a notary public. You will then mail the completed form to the Florida Office of Vital Statistics. I have linked below to both the form and the instructions from the Office of Vital Statistics.
I cannot comment on whether you should wait until after your divorce from your husband is finalized to do this because you have given no information about the circumstances of any disputes between you and your husband.
Best of luck!
PLEASE NOTE: These comments are for informational purposes only and do not constitute legal advice. Actual legal advice can be obtained only after consultation by an attorney licensed in your state. Answering this question does not create an attorney-client relationship or otherwise require further consultation.