I don't have time to write much, but I just wanted to say that YES, she sounds gifted. She also sounds like a ton of fun!!
I have a 24 month old who is reading (actually reading not just memorized sight words) and very verbal. Having little ones that show how different they are at such a young age is pretty shocking, at times. I'm happy to see another parent with a little girl with similar skills - although I think your kid might be more of a ham! So cute.
Let me recommend a book that changed my perspective. It was recommended to me by the good folks here. It's called 5 Levels of Gifted by Dr. Ruf.
http://www.amazon.com/Levels-Gifted...ref=sr_1_1?ie=UTF8&qid=1335376436&sr=8-1 It clearly explains the different levels, or degrees, of giftedness and gives you examples of what children in these various levels are doing at different ages. I think you'll find it's a real eye-opener. Your daughter is extremely gifted from the sounds of it! It's great that you are recognizing that now so you can prepare for what might be coming in the future!
OK... my time is up. Last word of advice on how to encourage her: For now, just follow her lead.
