Why would she have a heart attack? If rabbits are incredibly scared etc. then it is possible for them to die of fright, but i wouldn't imagine introducing a puppy to the family would inspire such an extreme reaction.
It's good that you have concerns, but rabbits, cats, dogs etc. can get on very well. Millions of people have two out of the three, and many people (like me) have numerous numbers of all three with absolutely no problem.
The cats curl up asleep with the dogs, the rabbits nuzzle the dogs, the dogs cry if they can't reach the cats through the stairgate because they want to nuzzle them etc.
My rabbits willingly approach and snuggle, sniff etc. the cats and the dogs
I understand because she is slightly older, it may be more of an extreme change for her, but 5 and a half years old isn't particularly old for a rabbit, and there should be every possibility they will get along fine.
However, as elrowen said, some dogs and rabbits just won't get on- the dog might always want to play rough with the rabbit, or the rabbit might be aggressive towards the dog on every meeting.