What is the purpose of Medicaid?
Medicaid is to help those people who are not offered health insurance thru their employer or cannot afford it.
The short answer is, you don't. Medicaid (and your fellow taxpayers) expect you to use your assets to pay for your medical care. The only way to "protect" your assets is to transfer them to someone else prior to the time you expect to need Medicaid (for nursing home care, at least 60 months prior), or spend them on some legitimate purpose for which you receive "fair market value."
There is no automatic transfer of eligibility from one state to another. You cannot receive Medicaid in more than one state at the same time; so, you will need to terminate your Medicaid coverage in NJ. Get a letter from your NJ Medicaid office to that effect that you can give to the FL Medicaid office when you apply there.