The short answer is no - not without Court permission. If you are on probation in Florida, you must obtain the permission of the Court before you travel. Probation, by its very nature, will likely restrict your movement to one county (the county in which you reside). In order to travel from county to county (for instance, you work in Miami-Dade County but live in Broward County), the Court must permit that. Normally, you will want the judge to put in your probation order that you can travel to and from such-and-such a place for work purposes. I recommend doing that at the time you are placed on probation (your plea hearing) so you don't have to come back to court at a later date. This applies to misdemeanor and felony probation.
If you want to travel, either domestically or internationally, while on probation, you must obtain a court order. Your attorney can help you in doing this.
If you want to have your probation transferred to another county, the judge can order that. If you want to have your probation transferred to another state, that is a process that is done internally through the Florida Department of Corrections (known as Interstate Compact).
Do not travel on your own while on probation. You could find yourself facing a probation violation. If you need to travel for work or just want to take a vacation, that is fine. Just make sure you ask the judge first.
Eric Matheny is a criminal defense attorney serving Miami-Dade County, Broward County, and Palm Beach County.