Remind yourself she is two, very young. I am a FIRM believer you wait until all the signs and readiness are there before you start potty training. I have successfully trained two and didn't even start until they were headed or close to 3. VERY RARELY does it happen in a day. Her body ahs to be ready, her bladder has to be capable of holding it and that is something she or you have no control over.
Get her a cover for the big potty too. Little pottys just give them another adjustment when they outgrow it and move to the big potty. Desensitizing her to the big potty now will save you. I just got my kids a potty cover seat and a little stool for the big potty. Never did the potty seat at all. That helps too when they go into public they are familiar with the big potty too.
Your daughter needs to be able to hold it, understand the urge and hold it until she gets to the potty, wakes up dry from naps and in the morning, be able to pull pants up and down and her body needs to be just as ready as her brain.
NEVER ask a child if they have to go,if you ask 99% of the time as they are busy playing and don't want to stop. As they get older asking is fine, early on not a good idea.
Just take her to the potty every hour and set her on it, ask her very nicely to "please try to go" if she does great, if not let it go.
I am against putting them in underwear until they are really ready. Doing so makes things more stressful, messy and makes it a difficult experience for you and she. When she is ready start with pullups first, they give them the experience of pulling up and down without worrying about pee or poop on the carpet. I did pullups first for both of mine and it made it just light and easy and no stress.
I ask moms do you want it to drag out and be stressful or once you start have it over with once and for all?
If you just wait, let her body get to where it needs to be, let her be ready, start with pullups and give it time you will be much more successful.
My son wanted a Transformer, really bad, I explained at 3 those were for big boys, he needed to be in underwear before the Transformer could be his. We did a sticker chart, charting every time he went on the potty. Within two weeks he was done, 100% done! He got his transformer, he was in underwear other then night. It took another few weeks for nighttime underwear to be on, but it was easy, simple, no pressure and HE DID IT when he was ready.
Don't rush potty training, when she is ready you will know.