IF the existing tiled floor is solid and sloped properly, you could use it as your preslope. This may make it higher than you'd like, but maybe not. Depending on the drain that is there, it's possible, but unlikely, there's enough adjustment to raise it to the needed level. To get it out and replace, you'd probably need an inside pipe cutter and to dig out some of the tile/cement/mortar around the existing drain to then have enough room to install a new drain.
Or, if you tear things out, there are other systems that can be used to install a new, long-lasting shower. In FL, with the heat and high humidity, my preference would be to use a surface membrane construction method rather than a conventional one. This puts the waterproof layer immediately below the tile so there's very little to get wet and what does can dry out faster. This leads to less mold and mildew. There are a bunch of 'system's out there, but to give you and idea, go here and watch the videos
http://www.schluter.com/5288.aspx. The benefits of a surface applied waterproofing system apply for all systems, but this gives you the highlights and an idea of the how-to.