Yep - totally normal - that is breastfeeding, and it is not being "not full" it is that breastmilk is th eperfect fod, so they have no problem digesting it quickly, unlike formula, which takes them longer to process. Sorry to have ot break it to you, I nursed my 2 kids exclusively till 6 months, and then we started adding in occassional formula and solids.....until we added in other foods, they ate basically every 2-3 hours around the clock....I think about 4 months old, they had one good stretch at the start of their night of about 5 hours of sleep, from 6:30 pm till 11 pm....then I would feed them, I would go to bed, and it would be every 2-3 hours the rest of the night and day.
I did use the book "Healthy Sleep Habits, Happy Child" By Dr. Marc Weissbluth, with both kids. Our oldest we didn't get the book till she was 9 months, and I was desperate for sleep, and we did CIO ( cry it out - called extinction in the book) right away, and it worked wonders, your baby is still too young for that, though.
Don't worry, she will grow out of it eventually, and this time is a drop in the bucket of her life and yours, try to enjoy it and work through it - take naps when she does, even if you are laying on the floor next to your 3 year old while she plays, take a short snooze if you can - it is harder with 2, I know. My duaghter was 27 months when My son was born....the first few months of both of their lives is a bit fo a sleep deprived blur in my memory - thank goodness I took lots of pictures!
Their little tummies at this point can't hold too much - a few ounces at most and they can get that from one side, in ten minutes. Let her take the lead.
Jess