You should be able to do pretty much anything in the garden now. You shouldn't have a freeze until after December where you are if at all. As long as you do it right you should be able to replant and/or relocate most plants. There might be a few, like camellias, that you might want to wait on, since they bloom in the spring, but even these can be replanted if you don't mind sacrificing some blooms.

It's getting to be a great time of the season to be in Florida. I see some of the gardeners up north are worrying about taking cuttings so late in the year. For us, we can take cuttings almost anytime as long as it doesn't freeze.

For Zone 9, you can transplant many things year-round, though during the summer you will need to stay on top of transplants and make sure they stay moist. But they get less stress from September through to April.

Tender plants should be planted sooner rather than later. If they are transplanted any time after October, it is possible they will not establish themselves enough to survive a light frost. If they do not get transplanted before November, it might be better to wait until March.

Hardier perennials and deciduous could wait until they go dormant, they will get less stress this way and you won't have to be as worried about watering. A good layer of mulch around the root zone will help modulate the soil temperature and minimize temperature swings.

However, in my experience, the absolute best time to do transplanting is when a Tropical Storm is coming. A week of steady rainfall is the best thing for transplants!