Couple of facts:
1) true that you do not start to lactate immediately, during the first 2 days the woman produces colostrum and not the actual milk, and these 2 days are fundamental to get that milk running.
2) if you breast feed, you keep on producing milk, no matter the age of the child. Of course once s/he start to eat other food, the milk becomes less and less until the production stops.
3) Fun Fact: if Hipster is looking for milk from tits, means that mommy still breastfeeds her. Good thing! The longer a child is breastfed, the better!