G.T.
Hmmmm...... is the babbling new? Often times babies like to practice their milestones while they sleep - much to our dismay!
Is she hungry at 4:30? If you feed her does she go back to sleep?
I can remember my LO getting up at 4:30 in the morning forever! I had to cut down on her nap time AND give her a later bedtime for her to wake later.
So she had a 1 hour nap in the morning, and a 1.5 hour nap in the afternoon. I also moved her morning nap later. Their first nap of the day - if it is too close to their waking time, then it seems like an extension of sleep, and it exacerbates the early waking.
Is she clearly tired at 4:30 or is she just done sleeping? That will help you know if she is getting too much day sleep.
Another thing to consider is room darkening shades and some white noise. I am waking at 4:30am because it is light out and those birds are chirping away! If she sees the light she might have a hard time going back to sleep.
GOOD LUCK!