Sounds like you might be a lucky mom! I think there is a misconception about potty training with some people thinking children have to be between 2yr & 3yr to learn the potty, but it just not true!! All children are different, so if she feels she's ready and you are ready, go for it! I do home daycare and most of the children in my care have trained at 18 mo. to 26 mo. somewhere in there.
Just keep up what you are doing for now. If she is truely into it start taking her in every half hour/ hour or so and letting her sit. I like to offer small rewards for pottying, but some kids don't need that sort of reinforcement, especially younger ones, but you could do stickers, an M&M (1), or a penny for the piggy bank, etc. If it is going well for a couple of weeks it will go smoother and faster if you switch to the trainer undies. Pull-ups are expensive and feel just like a diaper so they are kinda a waste, IMO. Another good thing with girls is sundresses! That way they can wear them without undies and still be covered (at home of course) and it is one less thing to worry about getting off at the potty!
There is no reason to rush it, you don't want to make her feel like there is pressure, but I bet if you keep on the same track she will do just fine. The biggest thing to remember is that SHE has to learn to go, you are just the leader! If you find it is becoming stressful for either of you, just stop and wait! It will make it so much harder for the both of you if it becomes that much of a chore. If you have any more specific questions you can send me a messgae privately....I'm sort of a potty guru!!LOL
Oh, and don't be alarmed if she won't poop in the potty. It is perfectly natural for this to take longer. And don't worry about night time wetness, it is not really a valid indicator for potty training otherwise we would have 5 & 6 yr olds still in diapers!!! Most kids take a little longer for nightime dryness.