Is she falling asleep while eating or after? If she's falling asleep while she's eating then she is probably not eating enough and that would be why she's waking early to eat again. I BF and when DD was younger she would fall asleep whenever she was on the boob so I would wake her up, change her diaper, and feed her some more to make sure she was getting a full feeding instead of just "snacking".
Also, 2 oz may not be enough for her anymore. When DD was 3 weeks old I was told that if we gave a bottle she should have 3 ounces, but that might be different since I BF.