You've gotten some great advice so far. The one thing I would suggest is this: The most important thing TODAY may be the person who is coaching LO, rather than the gym. I say that because my dd started at a rec gym that competed AAU and non-sanctioned. (I didn't learn about JO until she was 8yo.) As a 7yo, she had a GREAT coach who focused on detail and taught form correctly. The next year, she moved "up" and the new coach allowed lots of sloppy form. She learned new skills, but developed bad habits. I couldn't actually see the difference at the time, but it is interesting to watch old video and see how her form digressed. As a 5 year old, I think the MOST important thing she can do is have fun. However, if ALL THINGS ARE EQUAL, she might as well be having fun at the JO gym. Change is harder once she has friends and falls in love with her coaches. If all things are not equal (the other gym isn't as "fun", etc.) she should stay put. Too many young ones quit because they are required to work hard before they understand the relationship of hard work to results. Yes, they are stronger, better gymnasts, but what difference does that make if they quit? Our gym had two amazing 8 yo L4's who quit bc it was no longer fun. My dd is probably a year behind where she might have been if she had started at a "better gym", but, she is also still in the sport. We moved to JO when she was 9yo and could understand how tough conditioning made her a better gymnast...and was committed enough to be 100% on board with a more intense program. She LOVED the sport, and may have been fine with a tough program early on...but maybe not.
I absolutely understand where you are coming from. I competed in equestrienne sports as a kid/teen. My parents were not able to buy me a great horse, nor could they afford lessons. But it was my passion, and I was still reasonably successful. Still, I have wondered what my path might have been with different opportunities. Kipper is in her third and final gym (unless something crazy happens!) I am at peace that I have done everything I can to provide the resources she needs to reach her full potential. It's completely up to her, but she will never have to wonder what might have been if she had been at a better gym. My personal hope is that she stays in the sport at least through middle school. They learn so much from this sport, and I think each year she stays in is valuable. As an 11yo L7, College gym is not likely, but not out of the question, either. Her gym has a great track record for helping each gymnast reach their full potential, and they will train her to the best of their ability as long as she is committed.
A final note: While you are wise to educate yourself now, and choose the best gym available, I think a great gym will take any kiddo at any age and take them from where they are to the best they can be. Several have to come to our gym from others, spent a year getting stronger, then skipped a level or two to "catch up" to where they might have been if they had started at our gym. With relatively low hours now, as long as she is safe and having fun, you will not damage LO's future possibilities by leaving her where she is for another year or two. She isn't likely to develop habits that can't be fixed on such a limited schedule. I am still a bit of a novice in the world of USA gym, but I have already seen several incredibly talented young (age 7-8) kiddos quit due to burn out or injury. They may or may not have stayed in the sport if they were still having fun instead of working hard. Then again, there are some really talented 9-10 yo at our gym who have been working at a high rate of intensity since they were 6. It's impossible to predict! Whatever you do, KEEP HER WANTING MORE!!!! She should always be begging for more gym time and a desire to work harder skills. As soon as that changes, burn out and/or fear will take over. Best of luck!!!!