I think it's awesome that you're researching this and that you want to encourage your daughter in the areas in which she's talented.
If she is used to working with Paint then
any kind of professional graphics software is going to be quite a stretch for her. (As you said, paint is super-basic). But what she'll be able to produce will be so much better than anything she could ever achieve in Paint.
Personally I would recommend Photoshop. It's what I started out in and it's still my favourite.
I'd also like to reiterate what Etheryte said: her age doesn't have to be a factor. Going from Paint to Photoshop is going to be a leap, no matter how old she is, but if she's got the determination to learn it then there's no reason why she can't.
I also agree that it would be smart to download a trial - it's a lot of money to spend on something that will take a bit of perseverance to master.
Good luck choosing!
