I agree with everyone else - the need for the 4th puppy shot depends on when the others were given. Sometimes it's required if the other vaccines are given too early. Sometimes it's just vets over vaccinating. That's why you need to find one who will explain it all to you and let you decide. Doing your own research is good too so you know what questions to ask.
My concern was with the Lepto part of the vaccine. That can have bad side effects. If he gets a 4th shot of just the distemper that's probably fine. The 6 in 1 also includes unnecessary vaccines. Their bodies just can't handle it and it's not worth the risk of the vaccine side effects. And when I mean side effects, I mean it could kill your puppy - so that's why you need to find a good vet who will give you all of this information. I don't want to scare you, but that is why you should not go to the clinic and you should find someone who knows about small dogs.
I totally understand the moving thing. We are moving and I will miss my vet so much. I think I will have to interview new vets before I pick one.