I am very happy to hear that your daughter is beating the odds.
I'd use a 35mm SLR with a fast lens for this project. They are easy to use, unobtrusive, and quite capable in this situation. And the image quality they can produce is more than adequate for this use.
When my father died, I shot his body in the hospital. I got along very well with my father, and his death came as a shock. I decided it was probably a twice-in-a lifetime photographic opportunity (one for each parent), and that as hard it is was, it would have some artistic and emotional utility for me at some point. So I decided to seize the moment for raw material and sort it all out later. The camera helped me cope with the shock of the moment by giving me some sort of specific task to focus on. I stopped by home on the way to the hospital, and, preparing for the worst possible lighting, I loaded up my Canon F-1 with Fuji Press 800 and put a 55mm f/1.2 lens on it. I didn't have a meter, so I guessed. Ended up using f/2.8 at '60. I wasn't sure what to do with the pix, but as I expected, I figured something out some time later, and the project I did really touched some of my family members, and also made it into a juried show and won me a scholarship.
The point is that I couldn't have imagined being able to get the pix I wanted with any other type of camera. RF focusing and framing wouldn't have been good enough. Medium format would not have been as easily hand holdable, and likely would have been noticed by hospital staff. SLRs provide very accurate framing and focusing, which helps you out immensely in tricky situations. And small format gives you an unobtrusive package that excels in low light, and it gives you more D of F at a given f stop. You have to be fast, accurate, and fairly unobtrusive, all at close distances hand held in poor light. It's the perfect job for a small format SLR in my opinion.
I am glad that in this particular case, you are making art out of a new life, instead of out of death. Good luck with your daughter and with the project!
P.S. Other great options could be discussed at DPUG, such as a high-quality point and shoot digital camera like the Canon S95, and then inkjet negative transparencies. They are incredibly unobtrusive (completely silent, and smaller than a wallet), and provide great depth of field and good low light ability (S95 has an f/2.0 lens).