My suggestion is maybe you are putting er down awake when she is too tird. There is a window of opportunity that if you miss it, generally does not work :) I would put her down BEFORE she is appearing drowsy to you - usually by the time we see it, they're too tired. After she's been awake about 2 hours at MOST I would lay her down to sleep. This is what I did with my son and he has always put himself to sleep. I don't think I have ever rocked him to sleep once.
To those who are saying your baby is too young to sleep train - I don't think you're talking about full sleep training here. You and your doctor are talking about creating some healthy sleep habits. There is NOTHING wrong with doing so from the very beginning. The methods just are different at this young age, compared to say, 6 months old.
Get the book Healthy Sleep Habits, Happy Child, by Marc Weissbluth. I cannot rave enough about this book. I used it from day 1 with my son. It divides the book up into what you can be doing to help create a good sleeper at different ages - no where does it suggest your little one this age should cry it out all night or anything like that at all. It is seriously called The Bible in our house, haha!
Remember that sleep begets sleep in babies and children. The more tired they get, the harder it is for them to sleep. The more yo ulet them sleep, the more they will sleep. My son has always shown us this. Case in point - right now my son is sleeping and it's 8am here. For the past 2 weeks, he has been getting up wayyyy too early and unable to stay asleep past 5:30 or so. He had been going to bed around 7:15 pm. So last night, we put him to bed at 6:30 pm and low and behold......sleeping much MUCH later than he does when put to bed later at night! I'm not suggestiong your daughter is going to do this at her age - but my point is, the more you can do to protect her from being over tired - the easier your lives will be.
Good luck - you can PM me if you have any more ?'s about this as I was very successful with creating my good sleeper :)