Reddit mentions of A Treasury of Japanese Folk Tales: Bilingual English and Japanese Edition

this book contains a lot of famous folk tales that she would appreciate

this should be good for her to read to a 1 year old (old timey stories) and when the kid gets older he/she can read it as well -- in both languages. My kids (half japanese) were interested in more basic type of books at that age, such as your typical norimono type books, inai inai baa types -- peek a boo pop up books, animal books, etc etc... I am trying to remember off the top of my head but amazon doesn't have much selection (US version). If i were you I would take the general concept of "what books would I buy for a 1-2 year old" and go to a Kinokuniya if you have one local to you and see what cool books you can find.. (or order online)

I own a few beginner books like this. If you like folk tales, this is exactly what you're asking for: Treasury of Japanese Folk Tales - the stories are in English on the first half of the page, and on the bottom half in mostly kana with furigana over any kanji. It's a nice hardcover book with color illustrations on each page, so I think it's worth the price.
Clay and Yumi Boutwell have written Japanese readers that are very similar- furigana and kana text with definitions for each kanji/vocabulary on the bottom half of the page, followed by a full English summary afterwards. I own Hikoichi, Momotaro, and Inch High Samurai. I think the Boutwells' readers are good learning material but way overpriced considering how small each reader is. Since the Treasury of Japanese Folk Tales also contains many of the stories covered by each of the Boutwells' readers, it's a better bang for the buck (though missing the 1-1 definitions for each kanji/vocabulary).
I also own the red Giles Murray Breaking into Japanese Literature, but it's a bit above my current skill level since many of the kanji don't have furigana.
I have also looked into Kodansha's bilingual series, but since it's aimed at Japanese readers trying to learn English- manga have speech bubbles in English with no furigana kanji on the sides, but regular Japanese manga + English translated counterpart is more helpful since regular Japanese manga aimed for children have furigana.

I studied for 3 years, then stopped for the last 4...I can happily say that I've started practicing again.

I highly recommend purchasing books like these: Book 1 Book 2

You'll learn history/culture, familiarize yourself with relevant authors, be able to analyze how sentences generally translate, as well as learn words and practice reading! They give you kanji furigana, definitions, everything.

Edit: also, start learning your joyo kanji whenever you want to go above and beyond. It's from the Japanese department of education, the most commonly used/found japanese words. Often japanese newspapers are restricted to these, ~ 2150 kanji

:( Aww. Well, your public library might have some books for you. I know our does and I live in bat shit nowhere. You should give it a try :D!

Anyway here are some things I found: http://www.amazon.com/Alices-Adventures-Wonderland-Japanese-Carroll/dp/4042118038/ref=sr_1_1?s=books&ie=UTF8&qid=1346412718&sr=1-1&keywords=japanese+edition

http://www.amazon.com/Asa-yan-Midnight-Japanese-Shell-Rabbit_japanese-ebook/dp/B004TMCFN0/ref=sr_1_3?s=books&ie=UTF8&qid=1346412718&sr=1-3&keywords=japanese+edition

http://www.amazon.com/Treasury-Japanese-Folk-Tales-Bilingual/dp/4805310790/ref=sr_1_5?s=books&ie=UTF8&qid=1346412718&sr=1-5&keywords=japanese+edition

http://www.amazon.com/Princess-Kaguyahime-Kodanshas-Childrens-Classics/dp/4770020996/ref=sr_1_9?s=books&ie=UTF8&qid=1346412718&sr=1-9&keywords=japanese+edition