Good luck.
I found with my dd that it was easier on all of us to tell her that, although the proper place for poo was the toilet, we knew she wasn't happy to use the loo so she could always ask for a nappy if she wanted one for a poo.
It was a little different to your dd's situation, though, because it had been going on for a little while before we decided on the softly, softly approach and dd was completely hysterical at even the thought of using the toilet for a poo and had started to become constipated. We didn't give her the nappy right from the start so she'd had chance to get herself almost phobic about pooing in the toilet, and I think that's why it took us 15 months to get her to use the loo. I do wonder if she would have found it less traumatic (and gotten over her issues much quicker) if we'd just gone with the nappy right from the start.
Dd does still have pooing issues (she's 6 this month) so maybe we would have had the same problem anyway - but it made it more pleasant for everyone to go easy on her until it stopped becoming an issue for her. Once these things become an issue, they can be hard to get over.
Your dd is very young, and sometimes their fear of the toilet at that age comes from actually feeling the poo coming away from their body in a way they're not used to. They've never really felt it that way, they've never had quite the same realisation that it comes from inside them and it can take some getting used to. There's sometimes a sense that it "belongs" to them, and it's a part of them that's come away - with a nappy on they don't get that feeling in the same way.
Someone once suggested cutting a hole in dd's nappy and sitting her on the toilet, so that she had the familiar sensation of having her nappy on but still poos in the toilet. Once they get used to that, you cut bigger and bigger holes until they are literally sitting on the toilet wearing the waistband of the nappy! Dd wouldn't go anywhere near the loo to poo so that didn't work for us, but it might be something that would work for you if your daughter can be persuaded to sit on the loo with a nappy on. Don't push it if she won't, though.
She'll get there. I hope she gets on OK today.