Start asking around at the current gym, and keep going until you get somebody who can give you an answer. They, themselves should know what they're looking for. The critera may be vague and fluid, but that doesn't matter as long as you get an idea of the scope of the qualities you're looking for.
If age is one of their criteria, and there are age groups that I would shy away from, and it places your child in the "well maybe cuz you never know" category I'd suggest a shopping trip to find the best fit for your daughter at any of the other clubs in town. If instead, you hear that they "talk team" only when a child has shown she has a some ability, respect for others and herself, and works hard.....well that's a pretty good place to be.
In the context of the 2nd example, you're going to be far better off following the clubs lead even if it takes another year to find out if the team path is the right one for your child, because there are gyms that put any kid who can wear a leotard rightside out and frontside front on their teams, and collect team fees. Many kids are on teams as an automatic extension of the rec program, and are placed there with no chance for anything more than years of "participation" that go by as they see their dreams evaporate into reality.
I don't discount that participation is an important part of life, but have you ever heard a kid say "I want to do gymnastics so I can be a participant". I think most kids say "I want to do gymnastics and go to the olympics".....even kids old enough they should realize the reality of their age. So in a sense age is an issue because you hate to see a thirteen year old view their first back handspring as a milestone on their way to an olmpic dream. But hey, if a kid wants to participate and has the ability to see that reality, more power to them.
So stay put if you get a feeling the team path requires passing through a process that takes time, and you want your daughter to be selected on the merits of a process that often results in years of setting and reaching realistic and meaningful goals.
Just adding a bit of observation.......
If your dd started on the short side of "almost a year", she's making pretty good progress, evidenced by the skills seen at the levels 4 and 5. This could be either an indication of her over all work/passion/ability atributes or the program's ability to provide excellent instruction in a rec program setting, or a little of both. If you observe team kids that are happily working with their coaches on skills that impress you as advanced....you're probably in the right place, because they'll likely get to her unless they only look for the youngest talent.
Good luck to you!