First I would consider if you and grandma are able to pay and make the time commitment of gymnastics because it sounds like her parents can't. I don't have a problem with that, you and grandma just have to make sure you can do it moving forward. If she makes it on a preteam it will probably be more hours and more money, then she could competing as soon as in a year which is going to cost you for the warm up, tuition, meet fees, and coaches/booster fees. You might need to keep her at the smaller gym for a bit longer because of that. It would be fine to switch her as a 6 year old.