If you want to encourage her creativity and try to foster a genuine interest in photography, then I would be trying to get her to shoot as a photographer and not as a tourist, i.e. through the view finder rather than via the back screen (I'm not saying that the back screen isn't a valid approach to composing but it's good to learn the basics first).
I would also be aware that she won't yet know what her 'thing' is, i.e. what kind of photographer she will want to be, so something flexible, i.e. with an interchangable lens is probably a good idea.
You also want something simple and enjoyable to use as well as robust and second hand. At this price point and the brief I don't think it makes sense to buy new.
It's hard not to see an APS-C Nikanon as the obvious choice; I don't know the models well enough to make a specific recommendation but they are robust, flexible, dependable and cheap.
If you really wanted to be left field about it (and cool), go for a cheap body and then combine it with a really good but old manual focus lens. Manual focus will 'retro cool' and appealing but it will also teach her basic skills and make her think more about what and how she wants to shoot.
A mirrorless does have other benefits (I have only shot mirrorless digital the last few years myself) but they do suffer with being less robust; every time you change the lens you expose the sensor to dust and contaminants. With a DSLR, the mirror at least acts as a basic shield. Mirrorless need a good deal more care in their handling and they will be more expensive.
That said, and I will contradict myself on several points here, a very interesting option for someone so young but showing genuine interest in the medium, would be a first generation Fuji X100. It's very basic in that it has a fixed 23mm (35mm equivalent crop) lens and a hybrid electronic and optical viewfinder. It will be less flexible but it will be a joy to use and shoot with and it will encourage her to really think more about what she wants to shoot. It will be limited though given that you can't change the lens.
If your daughter was saying she really liked just photographing what and who was immediately around her, sort of 'street photography', people, friends, street scenes etc, then the Fuji would be an exciting camera to have and use.
If she doesn't know, then I'd stick to the DSLR route and go with a cool but high quality old manual lens.