This is just advice from a recent graduate.
As SOON as you can register with the Florida Department of Health and Pearson Vue - DO IT! You want your application complete before your college/university sends your information to the state so it can be married with your application file. You are placed in line for review according to the time your file is complete. Once your application is reviewed, then Pearson Vue is notified and will email your ATT.
Its important to note, if you are not registered with Pearson Vue when the state sends your information - prepare to go into a black hole. You will have to make contacts with both entities and coordinate the resending of information so Pearson Vue can issue your ATT. This will substantially delay your ability to schedule an NCLEX test date.
The moment you receive your ATT, schedule your NCLEX date. The dates fill up FAST and are first come, first serve. If you wait, you may have to test much later than desired and most GN programs require you to have your license in hand by a certain date.
I was registered with the state and Pearson Vue before I actually graduated and received my ATT about 2 weeks after graduation. Certain students who waited until after graduation to start the process waited almost 2 months for their ATT.
Hope this helps!