I think that by 2 1/2 she may have shown signs but you may not have not seen them, don't worry-you're a young, busy mom and you can start now. I taught 2 yr olds for 3 years at pre-school, what we did was start by taking them to the bathroom every 20-30 minutes-yes it feels like you are in the bathroom all day! When she starts to pee in the potty once or twice a day put her in panties. I learned this with my daughter-it worked the quickest,I put her in panties-and some days we went through every pair she had, but after about 2 weeks, she was doing very well. Also, unless you have already bought at small potty for her-don't. I used (at home and preschool)a potty seat that sits on top of the toilet and a stool so she could get on the potty by herself. And #1 rule is to be consistent-be consistent-be consistent, if not its going to take much longer, and stick with it, it won't happen overnight, it took my very intelligent daughter months to finally get there! You can do a sticker chart (mine was a piece of construction paper that said "Cassidy's Potty Chart" so you don't have to get fancy-she just stuck the stickers on wherever, it was easiest)or you could do rewards, like an M&M or 2. Just do it the same each time. Hope this helps.
Don't use pull-ups, they are a waste of money, they are just a diaper with pretty pictures, it prolongs potty training and they learn that they don't have to take the time to go to the bathroom if they are wearing one.