Mike,
You should be getting a 2nd set of shots pretty soon right? I would call the place (Mutts and Men) and see what their policy is. If all the dogs coming into the place have to be immunized, your pup will be ok I think. But I am not a vet!
I got conflicting info about shots before Fiona was totally immunized. I didn't take her out till she was completely finished with shots (16 weeks) and she has been fine with socialization, but if I had to do it over again I would have taken her more places earlier.