There are others here that are more knowledgeable than I, but I have spent literally HUNDREDS of hours researching cameras in order to talk myself OUT of a pro setup....in other words; I was looking for a camera that would produce good quality images, has a lot of flexibility, and a lot of features....without breaking the bank.
There are a couple "compact" cameras with some very grown-up features that supposedly are awesome.
The Canon G-10 comes to mind; but it was cost prohibitive for me. You could buy a Nikon D-40 for that price.
Anyway.......I started to focus on the features that were most suitable for my needs. One of the recurrent disappointments I have had with my "compact" cameras has been optical zoom. I always seemed to be in a place where I wanted to shoot something out of range. Granted, you don't need zoom for portrait shots, candid shots, etc......but when I go places I like to shoot things that are sort of distant as opposed to walking up closer to them.
With this in mind, I focused on "super zoom" cameras in the compact size.
I also wanted access to all normal SLR type settings.
I studied the cameras in this classification and settled on the 10MP Olympus SP-565UZ.
It cost about $200, has complete manual settings as well as a pretty damn good P&S mode. And it has 20X optical zoom!!!
I have had it for about two months and am pretty happy so far. I ALSO wanted to learn more about manual camera settings and this one has been very good for that. In general, the images are of better quality than most compacts/subcompacts and it is less picky when it comes to lighting, etc. I DO use the zoom quite a bit, I often exceed 6X zoom in my shots and it is delightful to just sit still and reach way out to capture something.
I also REALLY like cameras that take AA batteries....the hi capacity NiMH rechargables last a LONG time (I have taken 300+ with one charge).....plus if you get in a bind, drop in some straight AAs from 7-11.
These types are big enough to reduce the issue with sub-compacts w.r.t. holding them still but small enough that they aren't a real big deal to carry around. I have a medium sized case that holds the camera, extra cards, and three sets of batteries. I also have a pretty small case for JUST the camera if I know I am just going to go take a few shots.
Here is some info on this class:
http://www.dpreview.com/reviews/Q109superzoomgroup/
Anyway........it is REAL difficult to select an intermediate camera because there are SO many good ones; so I'd try to identify a few key features that would be important to your daughter and then go from there.