What I'd do is 'give' her a book.
You can't open the box without making it obvious you've done so. If she's the sort that likes to have a fresh box, I'd not do that. When she opens it, she can register it to her own account. MEANWHILE, you can make a 'gift' of a book to her email address. . . .you can even set it to be delivered when you wish -- so schedule it for Christmas day. She'll get an email with information on how to retrieve and download the book. Though you sort of have to hope she doesn't check her email before she opens the kindle or the jig will be up!
Wait. . .better idea. . .we're talking about your minor daughter.

So go ahead and set up her account NOW and buy some books on it. When she opens it and you help her register it the books will be ready to download. AND, though it might currently have your email address on it, when she's old enough, she can switch it to hers and take it with her. You need to specify a CC to start but can later fund it with gift cards so that she doesn't over spend.