I have the A710 IS... love it. It's a point and shoot (meaning that it has a good "automatic" mode for those who don't want to make any adjustments, just click photos), yet the manual shooting modes are incredibly versatile and you can do a ton of customizing. It's a great all around camera for beginners as well as those who are looking for some more high end features.
Pretty much all of the A-series cameras are the same, they only vary when it comes to the number of megapixels, the amount of optical zoom, image stabilization, etc.
I perfer the A-series because they do NOT have an internal Lithium battery, but instead use two AAs. I have NI-MH rechargables, but if you happen to drain those you can always pop in two regular AAs and keep shooting. With cameras with built in batteries (any "slim" or compact model of camera), if your battery runs out you're often stuck without a camera until you can recharge.
Oh, and to answer your question, you definitely won't be disappointed with the A590. It's definitely not a "cheap" camera and should take VERY good pictures. If your daughter is a little bit tech-savvy, she'll have a ton of fun playing around with its features, learning about digital photography, and transferring pictures to the computer to view/print/edit them. I would also recommend that in addition to the camera, you buy an additional SD card that's at least 2 GB (roughtly $10-$15), along with a SD memory card reader ($10), so that you can transfer pictures to your computer without having to plug the camera in and waste batteries when you do that. The A590 even includes image stabilization (hence the "IS" at the end of the model number), which helps you take pictures with less blur that can often come from taking pictures in medium-to-low light situations.