Heather,
You'll find a discussion of that issue in the
What about pets after the transplant? thread.
The consensus is that there's a small risk but pets are mostly safe to have around post-transplant if you use common sense about exposing the patient to germs. Some people choose to wait just a bit rather than have pets around when the patient first comes home, but it also depends on the logistical difficulty of having them cared for elsewhere.