It is very wonderful that you want to surprise your daughter with this most excellent gift. And I can only imagine how excited she would be to unwrap such a gift and thus make her Christmas quite lovely.
However, my very first bit of advice is going to be a bit tough: don't buy one for her without getting her input. If she has both talent and the desire to spend lots of time with her impending dSLR gift, then it stands to reason that she should help select the one for her. A camera can be a very personal item, which at first sounds odd. Camera? Personal? Really? Well I say yes. It is very important that controls and such fall readily to finger for the user. Real users don't want to have to feel around or look for the correct controls so that they might make changes. They need to be able to do it as if it were second nature. The only way to do this is for the end-user to actually handle the camera and see how it fits their hand, how the controls fall to finger tip, etc. Comfort is paramount and the only way you can achieve this is if she actually shops with you. I cannot too strongly suggest that you bring her in on your desire.
There is a second reason to include her: only she knows what is important to her in regards to equipment. She may, for example, be interested in a camera that is more compact than even an entry-level dSLR. She may prefer a more compact camera (but with the capability of shooting in RAW) such as the Canon G10, Leica Lux-4, or any other similar cameras. Or, she may indeed want a dSLR, but she may want to spend less money on the camera body such that she might obtain a better lens or lenses or vice versa. She may wish to try and incorporate a separate flash unit into your budget by sticking with only one lens for the time being. You see....as it will be her making use of the equipment she probably should have a say in what she is getting. I know it isn't as exciting as purchasing something for her and having her open it on Christmas morning, but I sincerely believe she will be even more happy to be involved in the process and will walk away with precisely what she wants within your budget (or she may opt to contribute if she can).
All that said, it would be hard to go wrong with a dSLR from either Canon or Nikon. They both make very good cameras, but more importantly they make complete camera systems (camera bodies, lenses, flash units, accessories, etc.) and have been doing so for a very long time. There are other companies in the dSLR marketplace (Olympus, Pentax, Samsung, Sony, etc.), who also make fine cameras, but there is a reason why you see professionals using Canon & Nikon: they work and have vast experience making cameras and lenses. I won't go so far as to say that Canon & Nikon should be your only choices, but they are likely easier bets for a variety of reasons. However, those persons I know who have non-Canon and non-Nikon cameras are not dissatisfied with their choices.
I imagine it would be easier for you if those of us responding to your request for help simply told you to buy camera X or camera Y and then list reasons why, but I believe this would be doing both you and your daughter a disservice. Most any dSLR from a recognized name will provide her with great service, but I strongly urge you to include her in the process so that she can obtain precisely what will work best for her particular talents and interests.
Whatever you do I wish you and yours the best this holiday season.