I also highly recommend the Buddy Belt. They have many sizes and half sizes, so you'll be sure to find something that's well fitted.
At such a young age, I'd probably go with the Buddy Belt 2 (it's the same design but made with a faux leather made of PVC or something). Buddy Belt 2 doesn't come in half sizes, but they have small ones for puppies. You put it on like a belt buckle, so it can be adjusted as the puppy grows. Once full grown, you can buy the original Buddy Belt, made of real leather. They last forever, so it's kind of worth the high price.
For me, it's something that's very important to invest in since I'd have a heart attack if my babies ever got out of their harness!!