Bella had her 3rd shot today and I carried her in her crate. There was a man with a 'puggle' puppy at about 8 weeks there. His puppy was on the floor on a leash. I am not sure if it was for 1st vaccination or second but I wouldn't be putting my pup on the floor of the vets. I did write about this on the Australian pedigree forum (that's not the name of it) and they said I was ridiculous and that all their pups go to the vet on a leash and said that crates at the vet are for cats.
Gosh, I don't really know the medically right thing to do, but my vet always told me to hold Brooklyn (not put her on the floor of the waiting room) until she got all of her shots...so that is what I did and Brooky was never on the vet floor until after her third vaccine (now she is and no worries). There is nothing wrong with bringing Bella in a crate to the vet, now or forever, so I think regardless you are just fine :) but I tend to agree that you should protect them that bit until they are older. I did not know this when I first brought Brooky in at 12 weeks, and I was about to put her down and the nurse came flying round the corner to scoop her up...not that they would catch anything she said, but better safe that sorry.