Ok, be careful because there are a lot of movie tie - in games out there. Watch out for those and avoid them.
Secondly, do not choose a game that looks like it was designed for the stereotypical six year old. I think this gives the reflection that the game was simply very well thought out in terms of its' marketing. Usually, these games are overly simplistic and shallow, despite the way they present themselves. A lot of developers market games for children that are not very deep, interesting or challenging; this means that it is usually better to choose a game that is not designed specifically for young children. If an Adult, as well as a child can enjoy a game, this shows that the game has something more to it.
Study the games that she already plays, if any, and which ones she enjoys. Also, you can take note of her general interests and hobbies and decide what genres best suit her.
On the whole, puzzle games, pet simulators and platformers tend to be the most accessible of all the genres. Evaluate the lifespan of games that you consider, too, and look on websites such as gamespot.com for useful reviews just to make sure.