All the evidence I see around me from various friends children says - leave it for as long as you can!
I felt some pressure when my daughter was 2.5 to start training. All her friends were trained. People talk about how marvellous it is that their DD is being trained at 2 as if that has a direct correlation to their intellectual and social development. What utter crap! Its just the same as training a puppy and it has nothing whatsoever to do with intelligence or anything else.
Like yours, my DD cares nothing for peer pressure or being a "big girl" or anything else.
I gave it a go at 2.5. DD is bright and willing and tried hard on Day 1 but the accidents and pressure distressed her as she wasn't ready to initiate trips to the potty herself. By day 2 she was throwing the potty across the room and begging for nappies. Lots of people say "Don't give in to them. They have to adapt." But, really, it was horrible for both of us and I was so relieved to give it up.
DD is now 2.10. I bought the Gina Ford potty training book and followed the advice in there. Essentially this meant 4 weeks of getting her to sit on the potty before her bath. After the first few weeks she did this every night and started doing some wees. There was no pressure because it really didn't matter. By the end of four weeks she did a wee on the potty before or after her bath every night. We did all the usual encouragement (stickers etc). For a month or so I would also show her the poo in her nappy, tell her how good it was and then put it into the potty or the toilet so she was used to this happening.
2 weeks ago I started full training (still following Gina Ford). She was dry within 3 days and has done a poo each day on the potty at her own instigation. I am delighted and so thrilled that I waited! A lot of my friends DDs who started 5 months earlier are only now at the same stage as my DD who has been doing it for 2 weeks.
So...very long reply from me...but stick to your guns. Delay, delay. Something happens when they get close to 3 which helps them understand lots of things, including pee and poo!
And good luck!