I have read that 80% of parents are correct when they believe their child is gifted. With those odds, if you believe it, it is probably true so act accordingly.
My son is 15 months and we say he is "tracking as highly gifted" since formal testing can not be done at this point. We have had a 2 hour phone conversation about our ds with Dr. Ruf and it opened my eyes so much!
As far as what we have done differently - we definitely pay more attention to the environment that he is in. Because he is in daycare/preschool we make sure he is in a place that allows him to progress by his development, not by his age. We have also found a school he will begin in the fall and hopefully stay through age 12. I am very happy we started looking early because it took us quite a long time to find (even though it is just 10 minutes from our home).
There is so much information that is out there and knowing my son was gifted early allowed us to get a good start and a good handle of the possible things we will face in the future. It also helped us know when the shack "advice" off. For instance, young gifted children are often labeled as "spoiled" by others and many people assume parents have pushed the child into learning. Knowing these are common themes, when we face them (as we have already) we don't let it get us down or have us second guess ourselves. That, in itself, it a blessing.
So, definitely assume your little one is gifted. And for now, let her continue to do what she is doing, but for you - maybe doing lots of reading about giftedness, learning about your school situation EARLY (will she be allowed to start Kindergarten early, are grade skips possible, etc.), and definitely try to find other parents (we are still working on this one :)).
