Liz, I think your plan sounds reasonable. It is an early morning, esp. for a teen! My dd who did it was 10 at the time, and we stayed at TL after surfing until about 1:00. I don't think we had anything else planned that day, but DQ would be a good option. Yes, you are able to stay and watch, but you need to exite and re-enter with your ticket to stay for the day. They escorted us out, but let us leave our towels on chairs before we left, so we already had a spot staked out for the day!
This was a "special" thing for her to do, and I told her if she wanted to do it again she was going to pay for at least part of it next time herself. The neat thing about learning to surf at TL as opposed to the ocean is it's a controlled environment, you always get the "perfect" wave. If I remember correctly she got 12 waves to try to ride.
In contrast, a friend's dd took lessons last summer and hardly had any waves to ride, it's the luck of the draw in the ocean. This wasn't in FL, but she said it was expensive, I don't remember how much she said it was though. You can always check out prices at Cocoa Beach too.
The instructors were wonderful, very professional and encouraging. DD loved it! I'm sure your guys will too! I think it was well worth the money.