Hi! I'm glad you found us! Your DD has lots of time to enjoy the sport even if she has started 'late'.
Predicting a timeline for advancement is a little tricky. To maximize her chances of going as far as she can you will want to make sure she in at a gym that more or less tries to advance students to a new level every year. Even among gyms that do a good job of moving kids along, there is much variability. For example, it's common to skip L5 or L6 because the levels are similar but not every gym does this and even if they do, it may not be appropriate for every athlete. In my experience most kids will end up repeating L8 or L9. Assuming your DD is part of a gym with the philosophy described above (skipping L5 or L6, repeating L9), she would be 17 or 18 at the earliest for hitting L10.
Talent of course is huge for longevity in the sport. Any athlete who reaches L10 is athletically gifted but showing great promise in L4 is no guarantee or predictor that they will have what it takes to get to L10. Things that can impact or slow a kid's training (besides lack of talent) include puberty (growth spurts and growth-related injuries hits some hard), desire to spend more time with friends or try other activities, a poor work ethic, mental blocks and injuries. A poorly timed injury or mental block can easily cause a kid who would have been on track to advance a level to have to repeat. Don't underestimate the impact all of this has on an athlete's training. Everyone is impacted in some way by each of these factors - even the most talented kiddos.
As far as D1 gymnastics - most are looking for multi-year L10's. For the highest ranked teams this means 4+ years as a L10. A first year L10 will most likely not be able to get a scholarship D1 spot, if anything at all unless they are exceptionally good on an event or two. I'm assuming by 'professional' gymnastics you mean Elite/Olympics...this is a whole other world. Think of the impacts described above x 1,000.
With all that said, your DD has plenty of time to enjoy the sport. She can enjoy lots of success while learning life skills that will help her through out her entire life. No one here can say whether she will make it to L10 but there is more to the sport than doing it just for that reason.