Making a Facebook page, website, twitter account seems to be the very basics. Doing anything more will cost money or time unfortunately.
First thing you could do is search twitter for kids game reviewers and send them a media package so they can review it. Send out press releases to review sites (all iOS/Android sites)
Another thing is to create youtube videos of kids using the game, seeing their faces while playing the game (provided they get super excited) could sell the game/toy.
Viral - this requires something that is awesome/funny/cute/shocking that people will want to share, cute could be something you want to play with and suits your target audience.
Also I noticed your Twitter page has one follower .... me! What you should do is add a bunch of people that matter ie review sites, toys related app sites. Most of them will follow you back and may even check out your game. (over the last few days I've gained 50 followers by adding people in the indie scene or review sites) While I'm not releasing my game yet, it will be helpful to have a larger audience to start with.
Free app of the day - there are a bunch of these promotional sites/apps, send them info about your game and one of them might like it enough to make it free app of the day but! understand most of them charge.
Other standard methods, pay google/facebook some cash and get some ads etc
Have a contact at apple (oh did I just say that wooohhh) knowing the right people actually matters.