First off, I want to commend you for recognizing that there may be a problem and taking those first steps to get your daughter the help she needs.
My first son is not "normal" although they tell us that he is not on the spectrum. He never played with toys. He was interested in doors, light switches and then by the time he was 2 it was electronics (DVD's, CD's, etc). He carried around CD's like other children carry around a stuffed animal. He also didn't interact with the other children in an age appropriate manner.
We started his testing when he was 3, so we missed the cut-off for ECI. We have used ECI for our younger son (just has a speech articulation problem). I would say they are a good place to start, but I think that it should be supplemented for more severe cases. Of all the places that we went to (school district, Our Children's House, neurologist and developmental pediatrician) Our Children's House at Baylor gave us the most answers and were most proactive in setting up a plan to help our son. I cried the day OCH gave us the results of his evaluation. Not because I was sad, but I was relieved b/c I knew he could finally get the help he needed. Ask, no tell, your pediatrician that you want a referral for a complete evaluation (they must have one to do an evaluation). They did a great job of recognizing and labeling my son's problems and providing therapy for those problems. Also, once we started therapy I met lots of moms going through simular problems in the waiting area. They were great at giving advice and recommending programs to try and not to try.
I know what you are going through and I can tell you it's not easy. We still struggle (our son is 5) with what to do for him. Those decisions that are so easy for moms with normal kids (school, activities, etc) are more complicated. That being said, there is not greater joy than to see your child advance and respond to the therapy. For example, my son would NOT color, draw, etc. In his Pre-K class last year the teacher would have to stay on him just to make a few marks on his paper. This year he has started drawing stick figures and writing his name without help. It is the most beautiful thing in the world to me!!
I pray that you get the help you need for your daughter. Always go with your gut, do NOT let others (your ped included) try to sway you away from what you know and feel.