I don't know much about the baby part, but I found this a long time ago(however, it is formal stuff, check out the "Learn" section).
Kids Web Japan
Also, for kanji learning, you WILL need to use this in conjunction with other kanji learning material, first of all, because this doesn't present you with all definitions for each kanji(at most, they only have one or two definitions), and second of all, because it only has up to the sixth grade. Here is the site:
https://www.msu.edu/~lakejess/kanjigame.html
I recommend Tuttle's
A Guide to Reading and Writing Japanese, because it includes all the definitions, on-yomi and kun-yomi readings, a few compounds, plus the stroke order and all kanji needed for complete literacy(the only kanji they don't go into are the kanji that the Japan Newspaper Association added for use in newspapers). I love this book. Finally, maybe LiveMocha can help a wee bit
Language Learning with Livemocha | Learn a Language Online - Free!. I hope some of this helps.