Thrush is contagious, this is why when a child has it, the doctor will tell you not to kiss the child on the mouth or face, and to make sure that the bottles are sterile for each use. It could be that she is getting it from the dog too, so I would have the dog looked at. Hope this helps, good luck to you all.
Very sorry to hear about your sisters health problems. I agree with tiggersmom. Also, using LISTERINE 2-3 times a day will help kill the bacteria that causes thrush. I have severe asthma and some of my meds have steriods in them, so, I get thrush sometimes too. I use listerine (as often as I remember) and my thrush has just about become non-existent. Hope this helps a bit too. Also hope your sister is doing well.