My experience with potty training one boy and two girls is that if you start training them before they are truly interested you will have a very long, drawn out training experience. My son showed an early interest in potty training so I took that as a sign he was ready, six months later he was trained! With my first daughter I tried to push it a little more. Although she was ready and she was fully capable (she had gone several days in "big girl" underwear) as soon as she realized it was important to me she regressed for two months. Finally she was fed up with diapers and the next day she wore underwear with no accidents, ever. With my second daughter, I finally got smart and let her tell me when she was ready to wear underwear - we skipped the whole pull-up ordeal. One day when she was a little over 2 1/2 she told me she was "all done with diapers" and that was it. She never had an accident and never went back to diapers, even at night.
I personally believe that pull-ups confuse the issue. If your daughter wakes up from her nap and every morning with a dry diaper then she may be ready, but until she really shows an interest in putting away all diapers and has shown a mastery of using the toilet, it is my opinion that you are in for a long process.
I'm sure there are many others out there who may have found more success with early training, but I found that putting an expectation on them too early led to a lot of tears and frustration - from both of us!