Babies were made to wake up in the middle of the night! I got 6 months to go then I get to enjoy the fun again heh. My littlest guy used to wake up in the middle of the night all the time, walking around bouncing him gently always did the trick for him.
From what ya were saying it just seems like it is her schedule to wake up at that time. like Birdgirl originally said try adjusting her daily schedule but do to the fact that babies don't sleep for long periods she is going to wake up at some different time in the middle of the night. In my opinion 3am is better than say a few hours before you have to wake up, by the time ya change her feed and comfort her, then get her to fall back asleep, you might not be able to get back asleep yourself heh. Although, parents of a baby always seem ready to get some rest