When can i walk my puppy?

My lhasa apso puppy has had his 8 and 12 week vaccines. The vet said that we would have to wait 2 weeks before we could take him for a walk. But my grandmothers dog was allowed to walk 1 week after her vaccines. (My grandmother also has a Lhasa apso.) will he be ok if i take him for a walk? Not a long walk but just around the block?