Hi S. -
Ah, the good old days - no REM sleep, baby up for a feeding every few hours - it's no fun, and most of us have been through it!!! (And it's really no fun to have your friends and acquaintances say, "Wow, your child isn't sleeping through the night yet? Mine slept through the night at one week/one month/since birth/whatever.")
I have a now 16-month old son, who was up twice a night until he was on rice cereal at 5 months, and then at least once a night until he was 6 1/2 months old, when we finally decided to turn off the monitors and let him cry for a few minutes each time he woke before going into his room (he wasn't waking up because he was hungry - he just hadn't figured out how to sleep through the night.)
One thing we did was to give him added rice formula (in addition to nursing), which helped fill his stomach a little better, so he wasn't quite so hungry. We also started using Huggies overnight diapers, so that he wasn't waking up feeling wet in the middle of the night - these really helped (I think the smallest size they carry is a 3). However, most books will tell you that the majority of babies don't sleep through the night until 6-7 months old (despite everyone you meet saying otherwise). Your daughter also could be going through a growth spurt, which may be making her hungrier. Peter (my son) went through one where he needed to feed every 90 minutes, round the clock, for a week and a half. I have never been so tired in my life!
Now that your daughter is starting on solids, you might want to give her both the cereal and milk right before she goes to bed, so that she has a full stomach.
If your doctor isn't worried, I wouldn't be either - although that's easy to say at 3:15 in the afternoon - it's harder advice to follow at 2:00 in the morning!
Best of luck,
B.