Re: 10 m.o. mostly BFing . . . I'm hungry all the time!
Can you put some of your milk into a sippy cup just to let her get used to it? My DD took a bottle, but we still gave her a cup to carry around and to start chewing on early. Eventually, we got her to take water and juice in it.
As for the eating, yes I agree with the more protein comment. It is hard to eat meat protein in the middle of the night for me, but I found string cheese or yogurt (if you can eat dairy) are good. Or a bowl of high protein cereal and soy milk (if you can't.)