If you ask 5 dif vets you will probably get at least 3 diff answers. Get it done as early as possible, usually by the time they get big enough and get some weight on them would be best, that's why they get it by 4 months and the males can have it done around that time also. If you can catch the male before he starts to exercise the muscle area to mark "spray mark", or get into the "habit" of it., you'll be able to avoid the hassle of him marking after he's neutered, (females and males have the ability to spray).
Since the humane society gets thousands coming in, their vets see alot of animals, more than your vet will see in his (private practice) lifetime I am sure. They need to make sure all animals are spay/neutered before being adopted, so they do it early also and I have seen LOTS of cats and dogs from the shelters, they all developed just fine. Big strapping animals some of them. Have it done at 4 - 41/2 months, like your vet says, they may actually keep up with the new research coming down the pike.
pixie-woo's animals are the big reason why they do it early, some do come into season early.