At 6 years old it’s more about having fun and building movement patterns than it is about techniques. Most 6 year olds don’t have the attention or memory to learn the way adults do. The kid’s belt system is different from adults so even if she gets promoted a few times, she can’t be a blue belt until 16. The extra kids belts are a way to keep them moving forward and motivated but still never put them on the same level as adults. Generally speaking though, I don’t see many gyms rushing people through ranks because tournaments expose that kind of thing. I’ve travelled all over the country for work and always try to train at new gyms when I do. I can only think of one place where I was truly disappointed in the training. If a gym has a competition class on their schedule then that’s a good clue that they are squared away.
Keep in mind that Bjj black belts are very rare unless you are in a big city. Most of the time I train there is not a black belt on the mats. At a very big gym you might see 5-7 at a class. Kids class is almost never going to be taught by a black belt. Usually it’s going to be a purple or brown who has their own kid in class or just enjoys teaching.
If a 6 year old can have fun, work hard, learn how to control their limbs, and build confidence then you’ve done everything right. Try as many different places as you can before signing up. Most will let you do 2-4 classes for free. Don’t take a single class and assume it’s a good representation of the place because attendance varies from class to class. It can change the whole vibe if only a couple troublemakers show up to your trial class. Ideally you would want at least one more little kid to be training so she can make a friend and have a training partner who isn’t twice her size. Don’t write off gyms that do mma/wrestling/no gi too. A lot of the kids (my son included) really love striking more than grappling and you would never find that out in a strict Bjj gym.
Some things that would make me suspicious are: long membership terms (1 year+), no trial classes without paying, requiring you to buy a gi from them with their logos all over it, requiring payment for belt promotions, kids going to the bathroom without shoes on, no live rolling/sparring (at least for the kids who are regular students, they may not let a trial class kid roll on the first day).
All this to say that there’s not a ton of bad gyms out there. If she vibes with the coach and other kids then that’s the most important thing at 6 years old. This is JMO as someone who coaches the kids Bjj and mma class at my gym.
Bonus if you start training now so that you will have a couple years experience when she is ready to start.
When we train BJJ we make sure to show what happens if the other party is striking. Often one night is/was used to train "other martial arts" boxing, MMA, etc
