It is important that you go and see your vet urgently. Indeed, it is possible that the rat was killed by anti-coagulants, which can consequently poison your dog. It is essential to go there before any symptoms start appearing because, if it is indeed anticoagulants, it will be too late to treat it (because anticoagulants prevent the blood from forming a clot to stop the bleeding even small bleeding). It is necessary to act within 24 hours after the poisoning. Your vet may do several tests to find out if your dog is intoxicated with anticoagulants or not. If these tests are positive, the main treatment will be administration of Vitmain K by your veterinarian. Hoping to have helped you, good luck.