Answer:
Well, I don't see why she won't let you, i can do all that stuff! Maybe look up on the Internet for gymnasiums wherever you are living, then hopefully your mom will realise how interested you are. She might be keen on the idea but doesn't want you hurting or breaking anything, this can easily happen in gymnastics, trust me. if you still can't convince her maybe talk to your dad I'm sure he'll manage to convince her if not then your older brother or sister if you have one, they could maybe talk your mom into it. If any of your friends do gymnastics I'm sure they'd love you to join, there moms could possibly talk to yours.
If she doesn't get convinced at all, there isn't much luck that she will let you start before Christmas maybe try again after, sorry.
Hope this helps and hope your mum is convinced, after all you do seem like you have done gymnastics for ages!