Nope .. it is a myth that you need to let a female go through her first heat.

Puppies are safe to spay/neuter as long as they are at least 5 lbs and healthy. We consistantly spay dozens of 8 week old puppies every week at my work and they all come out just fine!

It is better to do them younger. They bounce back a lot quicker. Some vets will not spay until the dog is 6 months, but there are several vets that will do it earlier. It is very safe.