Nobody's hair 'needs' to be brushed.
Well, you say that, but DS's hair would just be one large dreadlock if I didn't brush it.
DS also hates having his hair brushed, and always has. He has long, curly (finger-sized curls) hair.
We started with bargaining - watching TV, with snacks, I was allowed to carefully cut chunks off - he looked fairly awful, due to this being done in a rush, so not all entirely the same length, but meant that no brushing was needed.
When he got a bit older (older than yours), and he decided he didn't want it cut at all, I said that it had to be brushed, and we started off once a month, and now we do it once a week. First I carefully pull the tangles apart with my hands piece by piece, on damp hair (I use a spray bottle or a flannel), then I carefully brush/comb it through from the ends up, chunk by chunk, then I put intensive conditioner through, and he washes it out in the morning. It takes nearly an hour on a bad week.
It's not ideal, I think if I could get him to let me do it twice a week, then it would be much faster.
You just need to go slowly and carefully - whatever you can manage, and slowly, over the course of months, she'll get a little (only a little) more used to it.