A lot may depend if there is a civil no contact order still imposed. The Department of Agriculture can answer that question better since having a gun license is a privilege and not a right. You can always appeal.
Florida usually reports to all states. With respect to your probation, if you fail to report this to your probation officer in Illinois, they may use that as a basis for violating your probation as well. I am not an Illinois attorney and suggest you speak to one there before reporting to probation