I really wish I had my EeePC going through college. It's really small and really light. Being small, it's easy and quick to take out and put away, and it doesn't take up a lot of desk space. Being lightweight, it's incredibly portable, and so easy to just pick up with one hand. And because it's cheap, if it gets destroyed or stolen, you won't have to freak out as much as if someone walked off with a $2000 laptop. Battery life is almost twice of my full size laptop.
I have a pretty nice 15.4" HP laptop which I thought was fairly portable. But it rarely left the house since it was too much of a pain to lug around. Now that I have this EeePC, it goes with me everywhere I go, and easily fits in my glovebox in my car.
However, if your daughter isn't concerned with size, weight, and cost, then don't get the EeePC, since those are the primary reason people buy them. It's drawbacks are:
You need to buy an SDHC card if you plan to install any heavy-duty applications, because the 2GB/4GB/8GB drive is not sufficient for advanced use. I have a 16GB card that holds a lot of my data.
It's also got a tiny keyboard that takes some practicing. I've had my EeePC for about a month and a half now, and I can touch type with ease. But when I first got it, it was a challenge.
And then of course there's the fact that the screen is incredibly tiny. It's a nice screen though, with a much higher pixel density than most laptop screens. But at 800x480, some applications don't fit.
Other issues are very minor, like processor speed. Some people laugh when they hear I bought a new laptop with a 900MHz Celeron that comes underclocked to 630MHz. But it performs incredibly well, and boots up faster than my desktop or laptop (which are dual core and are much more powerful).
If you decide to get a full size laptop, don't get anything larger than 14.1", especially for school.