Everyone saying he should have just given her the living rabbit, isn't thinking about this in the long-term living with your monster-adjacent family member way. Like your vampire child can be perfectly healthy if you bring over a rootless drifter to be drained once a week, but the bodies and suspicions will pile up pretty quickly; instead the long-term solution is to setup a blood bank, where no one would notice a bit going missing from time to time.
Doing it this way gets him a new revenue stream, dish, and socially acceptable way for his daughter to get her needed nutrition. It even helps the adventurers with a new type of gathering quest.