My granddaughter, age 6, has expressed some interest in learning to play the piano. She's quite proud of being able to play a couple of scales I've taught her.

Any suggestions about the very first book for her?

There are several good method books out there. Because she is so young, I would start her in Faber & Faber's My First Piano Adventures. This 3 level primer woudl most likely be something she could go through rather quickly, but it focuses on a lot of singing and gives opportunities for movement ideas with the CD, which is a lot of fun for kids this age. Of course, having a teacher who can respond to difficulties that can come up and who also has many supplemental ideas that will aid in her progress woudl be best. Why not search for a good teacher for her?

"My First Piano Adventures" was designed and tested for 4-5 year olds ?

Also very fun AND pedagogical is the Piano Adventures Primer - plus these video examples and tips here:
http://pianoteaching.com/guide/contents.html

Such things all depend on where the student is developmentally. I've had 5 year olds begin with primer levels of books and do just fine, while others need to go at a slower pace. Sometimes the age indicates this, but not always. Again, this is why having a teacher who can interview the student one-on-one and make adjustments as necessary is important.

FYI, this is off of the site you referenced (Faber's website):
"Written for ages 5 and 6, My First Piano Adventure® captures the child's playful spirit. Fun-filled songs, rhythm games and technique activities develop beginning keyboard skills."

Thanks for your feedback. Based on your recommendations and checking out the teaching guide, I just ordered the Piano Activities - Primer.