I'm guessing it is probably because she drinks it so fast that she doesn't give it a chance to poison her body. He drinks so slowly so he gives it a chance to go throughout his body and kill him. That's my best guess, because I am no genius.
OK, so there are various reasons for this. One reason could be she took something that could counteract the poison. If she did, and drank it quickly, it would not have affected her. Her immune system also could have supported her for the little bit of time that the poison was within her.
