like matt said, it really depends upon what she wants to get out of the new camera. if she just wants a camera that will produce really nice images, but is not interested in learning more advanced shooting techniques, an slr may be overkill. but i do not think it's dumb to get an slr just because she is a beginner and hasn't used one before. when i got my first digital slr at the end of 2003, i had never owned a film slr and didn't really have any idea what i was doing with it at first. but i knew that it was something that interested me and wanted something that i could learn on and i could grow with. at first, i stuck to the automated modes set in the camera, but i quickly learned that there was an awful lot more to get out of the camera by learning how to shoot in the manual modes. but it does take a substantial amount of learning to do so.
the "slr-type" camera that matt mentioned may be a decent option. they offer much of the flexibility of an slr but they do not allow you to change lenses. An slr operates by having a mirror in front of the film or digi-sensor so that the viewfinder operates through the lens--you are seeing exactly what the lens sees and the camera meters through the lens as well--when you press the shutter, the mirror flips up and the sensor or film is exposed. i'm not sure exactly how the "slr-type cameras operate in this regard--the viewfinder may just be an electronic representation of what the sensor is seeing at any given point. related to this is the fact that an slr's shutter release is instantaneous with the pressing of the shutter. digital P&S's have a shutter lag that i found pretty frustrating--the electronic shutter is not as responsive. i believe the "slr-type" cameras have some sort of hybrid electronic/mechanical shutter--i'm not sure how responsive it is.
the inability to change lenses, however, is the main drawback of these cameras. you are limited only to the type of lens the camera comes with and its zoom. now most of these come with good lenses, with good optics and a decent to good zoom. so the basic lens that comes on an "slr-type" camera is actually going to be somewhat more flexible that the basic kit lens that comes with a digi-slr (the kit on the canon drebel only comes with a 3x zoom). (there are some other technical factors that play in to this--i believe the sensor on the slr type is physicaly smaller than a digi-slr so it's easier for them to build a stronger zoom into the camera).
as matt also alluded to, buying a digi-slr is really only the initial investment. if she really starts to get into shooting alot, the limitations of the most basic kit lens will become apparent pretty quickly--it has a very limited focal range (optical zoom in P&S parlance), is somewhat flat color-wise when compared to other lenses in the canon range, lacks some contrast and can be a little soft at times. so there is a decent chance that she will want to upgrade lenses in the future and trust me, this hobby is even more expensive than taping. there is ALWAYS something else to buy if you really want to. plus, with digital-slr's, depending on how you shoot there can be substantial post-processing involved. i shoot all my images in RAW mode--RAW is the direct sensor data before processing is applied to the image to convert it to a TIFF or JPG. now, this offers incredible flexibility if you are serious about your images--it's basically like being able to handle darkroom processing--you get increased flexibility in exposing the image more or less to control highlights and shadows and allows you to adjust the white balance of the image in post. then, once it is in tif format, i do substantial photoshop work on many of my images. imo, the true benefits of a digi-slr are lost without doing some measure of post processing. just like serious film shooting, development is part of the deal. i cannot just take a bunch of shots, take my CF card to walmart and get prints. you can set up the slr to allow you to shoot that way but you are losing an awful lot of the control of the image. the "slr-type" cameras like the s3 is do not allow you to shoot raw--only jpg, which is an enormous drawback for me, but it may not be relevant for her.
now all that said, like i said earlier, it really comes down to what she thinks she wants to get out of it. if she just wants to take really nice images in the camera with some flexibility in how they are taken, but no post-processing, and no additional lenses, the canon s3 is is a great camera to look at. i looked over its feature set and it is really nice at that price point ($450 from B&H). you get a lot of the flexibility of slr cameras with the limitations i mentioned, a very good lens with substantial zoom range, an slr-"feel", built-in basic image stabilization (which you will not get in a digi-slr) and out of the camera ready to print ability. it could be a good bridge if she wants to start getting into photography more seriously without making a bigger investment now. she could learn all the basics of advanced photography on a camera like that and if it is something that she really gets into, it makes the much larger investment of an slr kit down the road much more justified. besides, the price of digi-slr's continues to fall as technology improves--the lenses will always be the most expensive part of the whole deal.
no matter what you get, i think this book:
understanding exposure is a worthy companion present. it's the best book i've seen on the fundamentals of advanced photography. it explains what aperture, shutter speed and ISO are in basic terms and how the three come together to produce images. it gives multiple photo examples of how each affects your image. excellent book.
feel free to follow up with any more questions or if you need clarification on any of this stuff, either here or by PM.