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The biggest risk is the squirrel bringing fleas into the house. As long as your daughter did not touch the dead squirrel, there should be no worries. Rabies is also a concern, but the probability is pretty low. As long as your dog is vaccinated and no people were bitten, then it's not really a concern. I would just dispose of the squirrel in a garbage bag. Wear gloves when handling it, and you should be fine.
I hope this helps, let me know if you have any other questions.