You are right, demand = supply. But, I wouldn't wake up my baby at night, unless she was malnourished or there was some medical reason for that. Is she OK with her 3 hour routine? Mine had problems with 3 hours until she was 4.5 months old, plus she was nursing at least 2 times per night. She was mostly on 2.5 to 3 hours during the day. Also, remember that your supply is at its highest in the morning and babies tend to need to nurse more often during the pm hours so there is nothing wrong with squeezing in an additional feed if your dd would take that.
I have heard of supply issues at around 3 or sometimes 4 month mark. I think that too rigorous scheduling can lead to drying up, especially if a mom wants her baby to go by the clock and doesn't look for cues. But, if you are not letting her be hungry and she is naturally doing well on 3 hours, that is probably what she wants now. Some flexibility is OK, too. If you think she is not getting enough you can always do EAEASY. Another thing is that at around 3 moms many moms resume a more active lifestyle, do more housework and that can lead to supply problems, too. Also, feeling not full is normal after innitial first two months.
