A lot (most?) clubs tend to not honor most other club's training systems and levels. (exception being perhaps more formal clubs like NASA and SCCA where you might have an actual license or log book to prove where you stand)
This being a NASA school, they're probably requiring NASA solo certification, which you can obtain by simply attending a few of their track events. You'll start in their "HPDE 1" category with an instructor and move up from there. HPDE 2, I believe is solo. HPDE 3 is solo with more relaxed passing rules, and HPDE 4 is solo with open passing. (sort of like "gentleman's racing"... you're expected to allow the faster car to pass, but you're not required to point them by)
Read more:
H.P.D.E. - National Auto Sport Association - We drive harder
You can also get started with clubs like Chin Motorsports, PBOC and others. Many clubs run the Florida tracks regularly and are a great resource for practice time.