
It depends which worming preparation you use. The ones from the vet are far more effective than the ones you buy over the counter at petshops or supermarkets. I always worm my pups at 3 weeks, 5 weeks, 8 weeks, then every month till they are 6 months, and every 3 months for ever after that.
Worm eggs in poo don't become infective till 24 hours out of the body, so if you have been clearing up after her promptly, your garden should be safe despite your pup having mature worms in the gut (which it sounds like).