Hookworms are nasty, and I've known them kill young puppies in shelters that didn't treat them, so it's very good that you caught them.
Unfortunately, hookworm larvae live in soil. If you left any of the pup's feces in the yard this week, everywhere he pooped in the yard should be assumed to be contaminated. The eggs fall into the soil from the poop and quickly mature into larvae within 2-9 days. Then the larvae wait for a host -- they penetrate the skin of bare feet to enter the next host. That could be your puppy again, or you, or children in your home. Winter freezes will kill the larvae, eventually.
Even after you've cleaned the yard, you cannot
walk barefoot in the yard where he left feces, for the foreseeable future -- hookworms are zoonotic (meaning they infect people too). If you have young kids, convincing them they aren't allowed to go into a yard barefoot is a chore, but it's very important if you've had a dog with hookworms pooping in that yard.
After treatment, talk with your vet about keeping him on a monthly hookworm preventative for a while -- at least through the winter -- to avoid reinfection. Bag his poop until you get a clear fecal test -- and wear disposable gloves! (Remember, hookworm larvae are microscopic and penetrate skin...)
Your monthly HW prevention MAY
cover hookworms, depending which one you choose. My recollection is that Advantage Multi can be started at 9 weeks, and it covers hooks--but check with your vet. There may be other options. They all require a prescription -- your vet can go over your range of choices when you talk about HW prevention. My experience is that once a dog is clear of worms, if they are on Advantage Multi, they don't get reinfected.
CDC - Hookworm - Frequently Asked Questions (FAQs)