We did the same thing, trained our son when I was about 3 months pregnant with my daughter. When we trained my son we said no more diapers, and we didn't use pullups...although I wish I had at night. We take him to the bathroom in the middle of the night, it works but I can't wait until he gets up on his own to do this.
I would just put your daughter in the underwear during the day and while you're out. They have to know what it is to be wet...and hopefully not like it. That way they want to stay dry and go to the potty. I wouldn't use pullups at nap time either...make sure you cut the liquids before nap time and take her to pee a couple times before...she should be fine. And then when she wakes up take her to pee right away.
They are going to have accidents, just be sure to always bring spare clothes/underwear. You have to constantly be watching them and take them. We had the issue with my son that he gets involved with playing and wanted to hold it too long...so by the time he ran to the bathroom he would partially pee in his pants, on the floor and then finish in the toilet. They eventually get the hang of it and go on their own...just takes time.
Good luck!
P.S. I had my husband take a week off of work and we trained our son in a week...non-stop and didn't take him out of the house til he was trained...kind of old school training, but it worked.