Just curious... do you want her to wake up at 5:30 AM? I know some people are morning people and that's fine. I just want to make sure I know how to advise you.
Babies have a growth spurt at 3 months of age that completely throws them off. If you didn't have a routine before the 3 months, it's that much worse from that point on. So you want to get your baby on a routine. Tracy's routine is EASY: Eat (after they wake up), Activity (after they eat), Sleep (after they get tired from their activity). You should be sure you're doing this now. Once your baby gets used to it, she'll know what to expect. Also, if your baby is used to eating to sleep (I'm assuming she's formula fed) then you may need to wean her of this.
I'm not sure if you've read any of the Baby Whisperer books. If you have, let me know what else you need help with and I can give you some direction.