LLC formed in Nevada can it do business in Florida
In principle, you could use your NV LLC to hold a rental property in Florida. To do so you would need to foreign qualify your NV LLC in Florida, a process that would be more expensive than just forming a new FL LLC, but would make it a bit easier to manage taxes.
It is generally advised to have each rental property organized under its own LLC is the state where this property is located in. So I would say in your case its probably best to form a new FL LLC.