We had this problem too, when DD was coming to school age. I'd been trying to potty train her for so long - we did the Gina Ford potty training plan (which worked in less then a week for my other DD when she was two!), star charts, The Princess And The Potty, Poo goes to Pooland, ERIC resources, a poo/wee fairy...nothing worked. Like your DD, she was perfectly continent during the day and not having "accidents" as such, but she always had to have a nappy on to do a poo or wee. I was terrified that she would still need nappies for school. I think she was picking up on my anxiety and frustration about it too, which probably didn't help.
Anyway, what did finally work was cutting a small hole in her nappy (I cut a hole in all the nappies she'd need for the day and hid the rest). I popped it on, she didn't notice and jumped on to the loo...but when she did a wee, it "tinkled" into the toilet bowl, which startled her a little. I feigned surprise, examined the nappy and said "Oh dear, there's been a mix-up at the nappy factory...never mind, it's only a little hole". The next time she needed to go, she wasn't impressed to find that all of the nappies in the bag had a small hole in, but as there were no others she used them, and she quickly got used to the "tinkle". I cut a slightly larger hole in the nappies for the next day, and the next, and so on, until there was just a wisp of material left which wouldn't stay on anyway, at which point she decided she didn't need nappies for wees any more and could just use the toilet. Phew!
We had always used a different brand of nappy for bedtime and thankfully she didn't demand an un-holey night-time nappy to use for daytime wees.
Poos continued to be a problem even after she started school. Luckily she always pooed right after her bath/ just before bed, so there were no accidents at school. She would poo into her night time nappy, I'd put a fresh one on, and then she'd go to bed. I did wonder how we were going to break this habit, since she wasn't yet dry at night so still needed a nappy at bed time. In the end, a friend with a younger child sent me a triumphant pic of her DS's first poo in a potty. I showed the photo to my DD, and she did a poo into a potty (lined with a nappy) the following evening. From there, it was a fairly painless journey through pooing into an unlined potty, to pooing into the loo (but I could only flush once she'd left the room). She's eight now, with no toilet issues.
Good luck!