K.W.
Potty training is a process and if your daughter recognizes all those things then I would definitely say buy that girl a potty or potty seat (we really like the baby bjorn ones)
I bet if you start now--she'll be fully trained by 2!
Here's a book that may help you get started:
http://www.amazon.com/Early-Start-Potty-Training-Linda-So...
Now the author tells you about the benefits of starting potty training as early as possible (like from birth) which in my opinion, is a bit unrealistic (and ridiculous), but she also has plans of starting at different stages too (like the age your daughter is and my son was when we started). We've found it really helpful! and our son will go both poop and pee in the potty now (but he still doesn't even tell us when he's dirty or going-so your daughter is already more advanced than he is!)
Good luck! I bet you'll see immediate results!