I know many mommy's are going to have a fit about this one, but my mom didn't give us a choice. And neither do I. I started both girls at 2 but they didn't understand how to recognize the urge...so at 2 1/2 they figured it out and then I didn't give them a choice. I sat them on the potty at regular intervals regardless...it didn't take long before they told me when they needed to go...and I mean within a few days. They sometimes cried or whined a bit when I put them on and would tell me they didn't need to go, but they went 9 times out of 10. One is five now and the other is 3...both are very happy, well adjusted little girls and have no problem going potty by themselves. They both were very happy to go very quickly and considered themselves bit girls.
I did use treats for a bit too...a chocolate chip if they actually went on the potty...no chip if they didn't go. Did it tear at my heart when they cried a little...yes. But I'm the mommy and I knew they needed to go. I would just stroke their face and tell them that it was okay and they didn't need to cry...and when they went I clapped and cheared and made a big deal out of it.
I'm potty training a 20 month old I babysit now. She really liked to sit on the potty so I figured I would try for a week and see what happened. We started by spending the whole morning naked in the bathroom..(I have a big bath...but a kitchen does fine too...it is easier to clean the floor) I had the potty chair out in the middle of the room and I had a couple sippy cups of watered down juice. We played all morning and every time I saw her start to dribble, I put her on the potty real quick. It took about three days for her to get it. Then I let her fun around with those little thick, cloth training panties. She wet the floor a few times, but it was only a week before she finally realized that she could make herself go on the potty. Now I put her on the potty about once an hour...maybe I little longer if she hasn't been drinking from her cup. She will go potty for me everytime. It has been two weeks and she has even gone poop twice on the potty and will tell me on occasion when she needs to go...I just has to take break and run her to the potty because she came to me and said, "potty, potty". I took her and she went pee pee. Now I still sit her at regular intervals because she will get to playing and forget. She doing a good job and will cheer for herself when she goes....
I was potty trained at 18 months, as was my sister-in-law, her brother and the grandma of the little one I babysit for said she had her daughter potty trained at 18 months too.
It doesn't traumatize them. You just have to watch for maturity. After a few days or so do they recognize the urge? Do they get upset when they have an accident (I do make a big deal when they have accidents...by saying no, no Annabelle. Pee Pee goes in the potty..I make a stern face.) After a week or so can she go on the potty and make herself go? If you see these signs in your daughter, then she is capable of going. It is a matter of constantly reminding her that she's a big girl and going pee pee in a diaper is not acceptable. And make her sit on the potty at regular intervals. When she gets the hang of it she will be sooooo proud of herself.
PS Do not use pull ups. They are just diapers you can pull on and off. You put those on her and she will never figure it out. A little pee running down her legs is the only thing that will help her figure out the urge. I've seen kids in pull ups for two years and not figure it out. I've seen a child that was potty trained in a few weeks with pullups. I can name countless children that were potty trained before 2 and 3 with regular cloth training pants. They have to feel it to get it.
Good luck!!!!