yes dawn dishwashing liquid does work and it's not harmful to puppies. I was also told that Joy dishwashing liquid was better, but i've used both and found that they both work good. But she'll have to bath them now and then in 5 days because if any eggs are on the dog they will hatch.
Hope this helps you out
A vet told us that a long time ago because he said that you either leave the fleas and it could kill the puppy or make it ill. this is the safest way to get rid of them.