Kids are at high risk of getting hookworms. This can be due to ingestion of hookworm eggs passed in the pup's stools (since kids touch the dog, sometimes around the hind end, and don't always wash their hands before eating, or before sticking hands in mouths); people can also be infected by hookworm larvae that hatch in the environment. The larvae can be ingested, or can penetrate skin through small open wounds. This happens often when kids walk barefoot or play in an infected environment.
So if your puppy had any fecal matter on her coat and your kids are licking the coat, that would be a concern. The best way to minimize exposure is to teach the kids proper hygiene, such as wash your hands after you handle the puppy, and don't lick her. It's also very important to make sure and clean up the pup's feces from the yard as soon as she defecates... this will help minimize environmental contamination while the hookworm problem is still being treated.
I hope you find this helpful. Have fun with your new puppy!
I just re-read your question, and realized you're wondering about the dog licking the kids, not the other way around! I guess I was thinking about younger kids!
Anyway... the dog generally should not be passing hookworm by licking at the kids, but I suppose there is still a small possibility of transmission, since puppies often lick themselves and eat feces and such. Any transferred fecal matter could end up getting ingested. But it shouldn't be a big transfer method.
Sorry I misunderstood the first time! Everything else I said still holds true. :)
The adult hookworms inside the puppy will die off very rapidly (within a couple days depending on type of wormer). It's the environmental problem that can be difficult to deal with, as the eggs can survive for a long time (months) and are hard to get rid of in a grassy-type environment. That's why it's so important not to let them remain in the first place. As long as you pick up the poop soon after it is deposited, and before the rains might wash it away, you should be fine.
There are some good monthly products you can give the puppy to prevent re-infestations if you live in a hookworm-endemic area. Ask your vet what they have available for that.