Heya, [IMAGE'S LINK: https://flic.kr/p/rJeaoH]IMG_2935
Just a thought, I let my daughter play with my cameras and ultimately she always goes to my EOS-M. It's small. It's a touch screen. It's LCD Live View lets her look at things, and touch it to take an image--just like a phone. It's so easy that a 2 year old can do it. She happens to be 2 years old, turning 3 now. Point being, if you think about it, today's youth will be using touch screens and other such business more and more. If you want her to keep up with it, it may pay off to have more modern features that are similar to what she will experience elsewhere, such as with tablets & smart phones. The latest dSLR's have live view & touch screens. But, an EOS-M can be had for dirt cheap these days. $200 gets you the EOS-M and a 22mm F2 pancake often enough, and you can choose between some colors if you look around. Small for small hands. Works just like a smart phone if she wants it to. Can be a full manual camera if she wants to go that route.
So I'd look at the T4i, T5i, EOS-M, etc. You can usually find them around $200 (EOS-M)~300(T4i). I know it's more than your original budget, but again, the idea being the touch screen and LCD and all that. Again, just like today's smart phones & tablets.
I totally appreciate your daughter saved up to buy a camera. Maybe you can go halfsies on it. Unless she is already the kind of kid that absolutely likes clunky dSLR image making, it's worth considering something with modern features that she will already be super familiar with.
Just a thought!
Here's mine at 2, can't wait to see what she does at 9, and I wish you the best of luck and best images/memories to capture!
by Martin Wise
, on Flickr