Why do you want her to fall asleep on her own at such a young age? If she is sleeping through the night you have it made! I am only an expert on my one 19 month old, and I know every baby is different but it hasn't been my experience thus far that just because I do x with her, she will always need x. I know people say that if she is nursing to sleep then she will always have to nurse to sleep but I just haven't found that to be true. It hasn't been true with anything.
Absolutely don't CIO with a baby that young. All those stress hormones are bad for brain development and I don't think even the hard core sleep trainers recommend it before at least 6 mos. I believe you can find information on studies which found that on the Dr Sears site someone else mentioned. I saw one of the Dr Sears speak recently and he had a laundry list of studies on the topic.
I'm not sure if anyone mentioned the book "No Cry Sleep Solution" by Elizabeth Pantley. I found it to be a great book. There are techniques for younger babies and older ones.
Another thing to acknowledge is that babies and sleep isn't just a straight progression. She may not be sleeping through the night going forward, just because she is now. You still have so many sleep disruptions to look forward to: teething, physical and cognitive leaps, different seasons, etc. So having the skills in a book like NCSS may be very helpful in the future.