Hello Natk. Welcome!
If your daughter is in a good school situation right now, you may not really need to test her further now. (I think it's great that she loves school!) Does your daughter (DD=dear daughter) seem to have intellectual peers in her class? Does the school seem able to teach her at her level? Parents usually pursue further testing when there is a particular need, e.g., to help find appropriate educational options or if necessary for admission to a particular GT program or early entrance. But if your DD has other kids like her in class and is appropriately challenged, you may not have to spend money on further testing at this point.
Your DD did very well on the COGAT, though it is not a very good predictor of how a child would do on an IQ test; it is a quick and easy tool that schools can use to help identify GT kids. Some kids who have tested very high on IQ tests have tested poorly on COGaT, and vise versa, at least from the informal polls on this board. (You can search for COGAT here and find some more info.)
As for joining MENSA, it really depends on your area whether there are any good programs for children. There are pockets of active MENSA childrens' groups around the US; I'm not sure if Dallas is one of those areas, but hopefully someone local will chime in. DYS is a great program for profoundly gifted kids, and if your DD does qualify, then of course sign up. It's free. Will your DD's school do any testing for your DD if you ask? If they might, check the list of qualifying tests
here to see if the school is willing to administer any of these. From the info you have given so far, it does not appear that your DD has taken a qualifying IQ or achievement test.
I have a rule follower like yours, who will do just what the teacher asks and no more. He will try to get away with the bare minimum too. (The characters in all his stories have 3-letter names so he won't have to bother writing more letters!) The trouble with the rule followers is that I think the parents have to really watch to make sure they are being challenged. The teacher will see a great student, who appears happy. For us, we saw that our DS was doing work he had known how to do for years, and we had to advocate hard to get him more challenging work since he appeared to be perfectly happy at school.