Well congrats on your new baby!
In my opinion I don't really see anything wrong with bathing an 8 week old puppy. I would suggest using a tearless shampoo, be sure to keep the lather out of the puppy’s eyes. I like to wash and rinse the face with a washcloth. If you start bathing puppies when they are young, bath time will be a normal experience in their lives, not a traumatic experience.
Teddy's first bath was when he was 9 weeks and a couple days old. He did extremely well too, I was shocked! I was even more surprised when he calmly laid down during his blow dry and didn't move until I was finished. He enjoyed playing with his chew toy the entire time lol.