I am probably not a good measuring stick as I often function on 3 to 4 hours. Best for me is between 5 and 6. Beyond 7 hours, I wake up feeling sluggish and slow. I'm a night owl by nature, but I also like the quiet of morning and my days start early, so sleep is one thing that gets sacrificed. I'm trying to do better as I know sleep is important.
In your case, when you have a nursing infant, sleep deprivation is just part of it. My little guy never seemed to sleep more than 1 1/2 hours during those early nursing months. I was quite exhausted much of the time, and when I went back to work, it was really difficult at first.
People used to tell me to rest when the baby naps, but I never did. It was always one more load of laundry or dishes or a moment for myself to try and read (I was often so sleepy, reading was a monumental task)! But, if I had it to do over, I would have listened to those sages and tried to power nap. Maybe you can do that during the day, if you're not working outside the home? Get the other little ones out the door; get tasks done while baby is awake, and then rest when baby naps.
I'd like to be able to tell you it will be better soon, but I don't know how old your baby is. Once the baby starts to sleep in more solid blocks, you'll feel better. Until that time, go easy on yourself and rest when you can. You may want to check out the book "Healthy Sleep Habits, Happy Child," by Marc Weissbluth, M.D. It was really helpful book on family sleep habits.
Good luck and rest when you can!
J. F.