Wait until the weather is cooler. As a general rule in FL, don't do anything other than water during July and August (don't even fertilize, everything will fry), and don't take cuttings or move plants until the end of October if the weather has started to cool (or if you are in N. FL). I often waited until Mid-November to take cuttings or move plants. The heat is just too intense this time of year for the plants to take under the added stress of moving.
November -April is a good time to move plants or take cuttings. Of course, if a freeze is expected, get those tender plants indoors!
Florida and fertilizing is a fun thing to keep balanced. With the sandy soil everything you add just drips into the aquifer every time it rains. I fertilized general plants once a month, more for tomatoes and heavy feeders I was trying to push before the weather either got too cold or too hot and killed them. But I didn't fertilize things in pots much, especially in the hottest weather. If your plants really need a boost give them a gentler 6-6-6 and water it in well.