She might want to try contacting her local Mensa group even if they won't take GAI. Many chapters will allow prospective members to attend events and she could always see if it's a group with whom she'd want to hang out. She could take the home test to see if she'd have a decent chance of passing the Mensa test which would be a good alternative to submitting prior proof.
The only thing I can say is that many active Mensa members are older than your dd. I didn't get actively involved until I was much older b/c I was the odd token young person. Even now, my local bunch has just in the past year gotten a group of us in our 30s rather than 60s who get together at a coffee shop once/month. The Annual Gathering is in Portland this summer and the AGs do tend to have more teens and active teen events. If you are anywhere near there, that might be fun to attend. We are usually happy to have interested prospective members at the AGs.
