After you establish your domicile (your main, primary home) in Florida, you can only be taxed by New Jersey on New Jersey "sourced" income. You establish your domicile in Florida on the date you begin living there with the intention (as evidenced by your actions) of making FL your new permanent, primary home.
One example of income "sourced" in New Jersey would be income earned from work actually performed in New Jersey.
Also, a capital gain from the sale of property located in New Jersey is taxable by New Jersey, regardless of your residency at the time of the sale. Your capital gain from the sale of a home in NJ is calculated the same way as it is for federal tax purposes. In other words, NJ will tax only the amount of your capital gain that is taxable on your federal tax return.
If you do move your domicile.to Florida, then you will have to file a part-year resident NJ tax return for the year of the move. All your income up until the date you establish your domicile in Florida would be taxable by NJ.
This NJ tax publication details NJ's rules on these situations:
https://www.nj.gov/treasury/taxation/pdf/pubs/tgi-ee/git6.pdf
Note that if you spend 183 days or more of a tax year in NJ after your move to FL, then NJ will consider you to be a "statutory" NJ resident, which would make ALL your income for that year taxable by NJ.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
