I am looking for those services that come at your door and exchange one small glass empty bottle for a new one filled with fresh milk.
If you want truly local Hsinchu farmers, then this seems to be the farm:
They deliver to Zhubei, but it seems like you would need to call them to order.
Most organic stores seem to carry milk from Goat Barn, which is a farm based in Zhanghua. I assume the organic stores verified they use real goat milk and not just reconstituted from goat milk powers. You can actually buy them off the shelf at some locations in Zhubei
自然法則竹北店 03-6573010 竹北區文信路371號
樂菲有機超市 竹北店 03 658 3731新竹縣竹北市文興路349號
Or have them deliver to your door: