The testing is expensive and really not recommended until you need one to get her into a gifted program. If it's done in school, it's free to you. Paid private testing before that is more for big-city folks who need a score to get into a prestigous pre-school.
About systemacially teaching her, you'll get folks on both sides of the fence. I'd guess 1/3 says yes, 2/3 say no on the few boards I've looked at. And half of the ones who adamantly say "no" approve of offering her self-correcting educational software such as www.starfall.com. Even the 1/3 who say yes say don't make it a chore for her.
Pre-school, well. That's so individual. I read somebody once say that she was very happy to have her baby at home with her, until he turned three! Then he needed something more than she had for him and found a preschool.
I'm a stay-at-home mom. I like pre-school education. So, if you chose that you want to teach her something ask me about resources. Oh, you're so lucky to have such a fun-sounding girl who obviously makes you very happy.


Youth lives by personality, age lives by calculation. -- Aristotle on a calendar