The child is a legal resident of FL, so FL has jurisdiction.
You might inquire about the possibility of an appearance by telephone.
It is possible that the Mom has applied for state assistance and the FL Dept of Child Services, etc., is the entity bringing this action. Your private agreement may or may not conform to state guidelines. Since it was never submitted to the court, there is no way of knowing.
Additionally, if Mom has applied for Medicaid or similar services, the State may very well want to know why you are not covering this child on your employer's health insurance plan, assuming you have access to same and are not already doing so.