Congrats on getting your doll! I like her impish face!
With the wig falling off problem, silicone wig caps work nicely but a lot of people, myself included, just use x-wide rubber bands.
As far as where to get the wig caps, Denverdoll has them:
Volks also makes sticky strips that a friend of mine swears by:
VOLKS USA, INC. | VS Doll Wig Stopper/ SD Pitatto Wig
If you send me a private message with your email address I can send you an invitation if you'd like.