I would agree with the links to the other thread, but that was for an 8yr old.
For something that young, anything to hold her interest. Blinky lights and something interactive. The snap circuits are a good idea, but she;ll be more interested when it does something like blinky or move something. The important part is she understands that she herself made it happen and that she could do that kinda thing. But at around 1, come on it's not in the terrible 2's yet.
Something I have always loved and is the perfect project from people like us and down to the kids, it this one:
[can't seem to find the link]
It's on
http://letsmakerobots.com/ but I had it bookmarked but it might be lost in time now, I'll explain the jest of it anyway.
Well, it was an Arduino with a couple servos to roll around on. But, it had some headers and color coded wires. Such as red is stop, green is forward, yellow is left, blue is right, and white is reverse. There are multiple of each color and enough headers to plug them all into, and it steps through the first header till the last and then stops, or loops if you wanted.
The kid can plug the wires in how ever they like but they know if the green wire goes first it moves forward. Then they can make it go where ever and know why it goes there and such. They might get curious and want to know how it works blah blah blah.
If it would be a boy, how about a bomb defuse prop/toy. He has to pull the right wire before it goes off, and he can set the time limit and stuff. Make it a game, defuse the bomb or clean your room. Make it like 6 or so choices of wire to pull, and have it be a random wire every time. So the house always wins (at least over time) cause of rng.
Now once they get to like 6 or so, then show them code and more intricate things. But the thing is, they need to see results. They need to know they are actually doing something.
$0.02