Yes, unless there is an order of the court stating otherwise the mother of a child born outside of marriage is the natural custodial of and for the child and she may travel and make other decisions regarding the child without legal regard to the father.
Daniel Bachert, Esq.
The Bachert Law Firm, P.A.
330 Clematis Street, Suite 222
West Palm Beach, Florida 33401
Please be aware and advised that this public forum is designed to provide only general information, to give you a basis of legal knowledge. This public forum does not give you attorney-client privilege. You and I have not entered into an attorney-client relationship. I am not responsible for your legal rights and this answer is based solely on the information you have provided in your question and as always, I would advise that you arrange for an in person consultation with an attorney from my firm or another Family Law attorney familiar with Florida Family Law who can analyze the specific facts and circumstances of your case more closely to better advise you.
If the parents are unmarried, the law in Florida is that the mother has all legal rights until there is a Court order declaring the paternity of the child. As the natural guardian of the child, you are free to go where you want with the child. Hope that helps you out. Have a great vacation.