The answer is basic biology.
No female animal (including humans) naturally gives milk without becoming pregnant and giving birth first. True with cows, true with goats, etc. It's not necessary to have a billy if you can get one on loan for stud service. My younger brother and I both have nanies and share the billy. Keeps him happy.
Doe goats come in heat about every 2-3 weeks until bred. then will start coming in heat again within 2-3 months of giving birth or once the kid is weaned--and yes you can milk it while it is still nursing the kid, just leave half for it. Milk for 10 months, stop until after the kid is born, and them begin milking again. They are being milked at the time they'tr bred and until a month or 2 before giving birth. 2 Nannies can keep a family of 4 in milk, cheese, and ice cream pretty well and are a lot less trying than cows. A billy can preform almost as well as a donkey when it comes to pulling (pull a grown man in a cart) but can only pack about 75 lbs on its back.