If your dog just licked the grape, he/she will be just fine, even if it's just a little guy/girl. He/she would have to actually eat multiple grapes (or raisins, just FYI) for him/her to get sick. Take a big sigh of relief and enjoy the rest of your day with your pup!
Source: Myself -worked as vet assistant, pet care lead at pet resort, pet sitter, pet grooming assistant...I could keep going but basically, dogs are my passion. I try to help others when they have a concern with their pup. :-)