According to my map Tallahasse is about 500 miles from Miami. Travel time was estimited at 9 and half hours, quite a commute.
Does Miami offer year round schooling in either thier public or private schools? This would give your child 3 months with you (while in school) and one with dad (off-track). There is also home schooling, this would allow your child's schedule to be more flexible. Consider these options if they are available to you.
You could also meet dad half way, once a month, twice if possible. Is there some nice city midway between tallahassee and miami to either spend one weekend a month or to simply meet and ...for lack of better words...exchange custody of your child?
Working out a custody/visitation in your situation isn't going to be easy on you, your ex and especially your child, but maybe if you keep an open mind and a focus on what is best for the child and parents you can make it work.
Good Luck