It could very well be that she is allergic to the puppy. Normally, it's not the hair of the animals that people are allergic to, it's the dander. Dander is actually tiny flakes of dried saliva from the animals grooming themselves. If the puppy was licking her, and especially if the puppy was licking where the rash is, then that's the answer. Sometimes when people are especially allergic they will get red or break out in a rash wherever the animal licks them.
I would still make an appointment to take her to the doctor to be absolutely certain of what this is. Is she taking medication for anything? If so, then the doctor needs to be notified IMMEDIATELY as a rash while taking medication can indicate a serious adverse reaction to the medication.
I hope whatever it is turns out to be nothing serious and your granddaughter is back to normal in short order!
Ghilly
The allergy would more than likely be from the dander on the puppy. Start with a really good bath, and rinse, rinse, rinse to get all of the soap out. Make sure he is squeaky, literally, clean.
There IS a trick that you can use to keep the dander down if you would like to try it so as to not have to rehome the puppy. It can't hurt and it might enable your granddaughter to be able to keep her pet in spite of allergies. Make a batch of tea. Make enough to fill a large pitcher and let it cool down to where it is only lukewarm. After you have bathed the puppy, rinse him with the tea. Don't rinse out the tea, just let the dog dry off. Naturally you don't add anything (sugar, cream, lemon, honey) to the tea. For some reason this works to keep down the allergens. I know several people who have had great success with it.
Ghilly