If you have not already done so, check out packing.org to see what your state's laws are on carrying in a hospital/medical facility. If it is illegal, it should also tell you what the penalties would be if your daughter "forgets" and carries anyway. As many will say, sometimes it is "better to be judged by twelve than carried by six."
My wife is considering getting her CCW. She'll try out my S&W 642 to see how she does with it. For me, the recoil isn't too bad but she may not like it. If that's the case, she does have her eye on a Beretta Bobcat semi auto in .22LR. The thing she likes about them is that they have a tip-up barrel that you can load a round into, then you insert the magazine and flip the saftey "on". If it ever has to be used, all she has to do is remember to flip the saftey to "off" and pull the trigger: the first pull is DA and all following are SA. It may be worth a look.
Like has been said by others here, provide guidance and training to your daughter, but let her make the final decision for what is right for her.