Oh nooooooooo!!! This is an issue that is better resolved sooner than later. With tiny babies, follow this rule: 1. Eat 2. Play 3. Sleep. Don't let her fall asleep while she eats, because she won't finish her meal and then she'll be hungry sooner. Put her on a schedule. Feeding every 3 hours worked well for my 2 kids. Feed her well, (keep her awake by whatever means necessary) then play for a while then encourage her to sleep by putting her down. When it is 3 hours after you have fed her, feed her again (wake her up if necessary during the day - not at night). My kids would cry for food, and I would tell them "10 more minutes, honey!!" and when it was time, I'd feed them. Read the book "Baby Wise" which will give you more info, I'm just giving you the synopsis. The exception to the eat/play/sleep rule is the last feeding of the day, when you can feed them and put them right down.
It actually sounds pretty mean and I never would have approached life in this way, but I had to return to work after my 1st baby was 9 weeks old, and I knew we'd both die unless we got some structure to our lives. It worked so well with #1 that I did it again with #2, even though I was staying at home. Some moms I know just feed their babies whenever they cry, but introducing the schedule made sense to me, so I could have control over the schedule of my day. The book really does explain it better, but it does require discipline, especially when first adopting the system (don't give in to the cries!!!) You may need some reinforcements to help you, too (dad, grandma, etc). But after the first week or so, you and your child will be sleeping better and eating better and controlling your life more.
Good luck!!