Hi M.,
I have a 17 yr.old son who is very sensitive, as well as a 9 yr. old who is also. When it comes to having pets, we have veered away from it because of the fact that even having fish for awhile was disasterous. Something in my body does something to the water and mysteriously the fish die off whenever I have to do anything with them that needs my hands in the water. My middle son would cry for hours, while the youngest would get angry and go off on his own. My oldest had cats off and on and where his grandparents lived was close to a road and well you can guess what was likely to happen there ><. He would always get upset and he still does over one of his cats. Every child is different though. And each child does bond with their pet. It may be best to explain the health of the dog to her and include her in caring for her (if her diet has changed due to the stroke, exercises, etc). Sometimes it is easier to deal with when you know what is going on. It is always scarier to try to "fight" something you don't understand or know. If you are religious, perhaps you can bring that into it also, maybe explaining that the passing is not something to fear but the next step in life and a level where she can still be guarding your daughter, like a guardian angel dog.
Going to school is wonderful!! More than likely you are going a lot of the hours during the day while your daughter is in school also?? If so, then you can come home and maybe the two of you can spend the evening creating dinner together. Have mother and daughter dinner nights. Then as she learns more, have it to where she cooks a few times a week then you cook a few times, then maybe a couple times you both cook....then there is always desserts to be made on the weekends and sharing a flour fight...LOL. Share in the laundry, shopping, etc...not only does it include her in things, but it also teaches her the things she will need in life as she grows up.
These are just a few ideas. I don't have a daughter, but I still do these things with my sons. You never know if they will need to cook on their own, and I want them to be able to take care of their girlfriend/wife if she is ill and to spoil her a bit as well *winks*. So not sure if it helps any, but that is my two cents worth.