I have a 13 week old puppy and need some advise about how safe it would be to dip her after a bath.

Please use a safer product to take care of fleas, such as Revolution.

I'm not a fan of flea dips or collars. Spot on treatments work the best, they are just a little pouch of liquid you put on the base of the dogs neck.
Your local vet or even pet store can help you select one before for a young puppy. I am a fan of Advantage but everyone has differing opinions on flea products.