As per the link to FWC, as long as you follow the guidelines, buy the non-resident SW fishing license, you can collect. What are you looking to get? To be 100% honest, there's not as much as you think. For example all stony coral (all LPS and SPS) are off limits to collect. There are a number of damsels, wrasses, 2 species of tangs, and about 3-5 types of angels, with a few others. They are not very easy to collect if you don't know how to.
The second, and perhaps larger issue is where you're going. Most of the Keys are part of a marine sanctuary, and/or parts of State/County/National Parks, all of which are off limits to collect. You will need to research where are planning to go, to make sure you're not inside protected boundaries.
I have collected tangs, angels, a baby snapper, a few wrasses, gorgonians, and some sponges.