You should probably expect it anywhere from 3 - 8 weeks, a buddy of mine got his back around 3-4 weeks just recently. My father's took longer due to a background discrepancy. The law in Florida states that they can only hold your money for 90 days, so your guaranteed before then.
Here are the laws regarding vehicle carry.
790.25 (3) LAWFUL USES.—The provisions of ss. 790.053 and 790.06 do not apply in the following instances, and, despite such sections, it is lawful for the following persons to own, possess, and lawfully use firearms and other weapons, ammunition, and supplies for lawful purposes:
(l) A person traveling by private conveyance when the weapon is securely encased or in a public conveyance when the weapon is securely encased and not in the person’s manual possession;
790.001 (17) “Securely encased” means in a glove compartment, whether or not locked; snapped in a holster; in a gun case, whether or not locked; in a zippered gun case; or in a closed box or container which requires a lid or cover to be opened for access.
To sum it up, put it in the glovebox. This ONLY applies to you without your permit, once you have it you can conceal it anywhere you wish inside the vehicle.