Its a water based product. So basically it will take as long to dry as it would take water to dry. Probably around 1 hour max in summer daytime conditions. Just keep pets and children off until it is completely dry.
Basically, what you need to look for is acute poisoning symptoms. If the puppy is lethargic, vomiting has diarrhea etc, then it may need medical attention. If not, then it should be OK. Hope this helps.