I assume you have milked before, and your goat is the first timer? It is quite normal for a first kidder to be a bit sensitive about you trying to milk her - and she will want to save the milk for her kid. Is she tied up - tightly? Have you tried feeding her about half an hour before milking, and then milking her, and she should stand chewing her cud?
I would expect a bit more than 5 tablespoons of milk to be honest!! Does it feel like there is more milk there after you have milked her? Sorry, this post is full of questions.
All goats differ in when they hit their peak re milking, and it all depends on feeding, weather etc. But, I would say, if she is having plenty of feed, and the grass is good, you should be getting plenty of milk around 6 weeks after kidding. Just remember the bigger the kid gets, the more it will drink .....thats the advantage of removing the kids from the female, you get more milk!!