I'm always amazed and the breadth of knowledge of some folks. What a great community.
I have no experience in BJJ or the like but i can offer this..I enrolled my daughter in Karate, Tang Soo Do, at the age of 6. Less than six months in. She hasn't quite taken to it like i would have hoped. There is a level of fear and nerves, like i said she is 6, that we had to work through because instructors are different and have different approaches and intensities. Try not to get frustrated. That part was hard for me. This was also her first go at a sport or activity outside of school.
Go to numerous classes, find instructors that she likes and can get familiar with. Also, it wasn't until she saw her first Black Belt female instructor that she became more engaged, albeit only a little more. It helps for them to see people like them doing what they are learning.