Awww, I'm excited for you guys. My DD is 7 and is on level 3 competitive team (training for level 4). Your DD's rate of progression will depend on a lot of different factors as there really is no set formula for all gyms (or even within one gym for that matter). Just tell her to have fun. Some things you can control to help her along ...
Make sure she doesn't miss practices
Make sure she's there on time
Tell her to follow directions
No crying or complaining
Be enthusiastic. doesn't seem like that will be a problem

And just have fun and work hard every day
At these early levels/young age it seems like the main thing they are looking for is a kid who is "coachable". Easy to work with, willing to follow directions and willing to work hard.