It sounds to me that you are doing things right so far. We had several starts and stops with potty around the same time. She would sit on it, but nothing would happen. We kept her in pullups until she was staying dry in them all day - except naptime. At 28 months, we decided to try underpants for a week. It was a disaster wash-wise... we gave her encouragement, and told her she would get it in her own time. She wanted to go back to pullups.
My daughter decided she didn't want to wear pull-ups any more around 30 months. We promised her she could wear big girl underpants if she stayed dry all day (which at this point she had been). We also had a book about using the potty that we read to her.
Like you did, she still wore her pullups at naptime. If they were dry after naptime, I didn't make a big deal about putting her underpants back on, she went potty and if she wanted to put them back on she could. I let her call the shots when it came to her potty training. We always praised her very using the potty, but never made her feel bad if she had an accident even in a pullup.
Her daycare had 3 toddler rooms and they could move up according to how they handled the potty (as well as other things)T2 started taking them to the bathroom in groups at regular intervals (and whenever they felt the need as individuals too) to get the kids used to going there and sitting on the potty. Potty training was big on the curriculum at this daycare. They don't pressure the kids, and I think they let the kids learn from each other.
By the time of her 3rd birthday she was in underpants all day and waking up dry in the mornings. Around this time the daycare also moved her to the preschool side. We had a couple of accidents due to her being to excited about being in the "big kids room". But she evened out. About month after her 3rd birthday we switched her underpants at night too.
I think you and she are on the right path to potty training. My least favorite part of it was taking her to public rest rooms, but those fold up potty seats are a life saver, I carried it in a bag with me everyehere. And Wipes, never leave home with out them. Get your daughter used to going out in public in pullups and that will help ease any anxiety for the switch to underpants. There was a time though, that I only shopped in stores with bathrooms.
I would say, from start to finish, it took 8 months (from 20 months to about 30 months old) for my daughter to stay dry and use the potty during the day. And about 6 months after that to switch to no pullups at night.
Good Luck!