Ok, the emotional side of it... DS4 was 9, similar age to your DD, when I first used the D-word, and he did find it hard to handle. It didn't help that his dad told him all sorts of nasty untrue stuff (the first he heard about it was when his dad said "Mummy's leaving us all to go and live with another man", which unsurprisingly made him burst into tears!). For the next two years while we went through the divorce process he was subjected to an almost daily barrage of emotional pressure, to say he wanted to live with his dad in the same house and didn't want to live with me and my "fancy man", and when he tried to say he would like to be with each of us half the time even his brothers jumped on him to tell him that wasn't an option, although I assured him it was. It wasn't an easy time for him at all.
The alternative, though, was for him to grow up thinking that the conditions he lived in, the stuff his dad said and did, were normal. Although with 50-50 residence he would be a fair time with his dad, he would also be a fair time with me, and I hoped that would be enough to keep him grounded. I told him as little as possible about our arguments at the time, but I did promise him that there was no "fancy man", and that he, DS4, was more important to me than my job or computer games. (I may have been lying about the computer games 
)
When we first moved he preferred staying at his dad's as it was the carer, atmosphere and general conditions (pathological untidiness and no baths!) that he was used to. Sometimes during the week with me he'd ask if he could pop round to his dad's, and I'd always let him as I didn't want him to feel he was a prisoner here. Later I found out he'd sometimes asked to go to my place in the middle of XH's week but wasn't allowed to. Not a huge surprise. Anyway, gradually he became more settled at mine, till eventually the school said they'd noticed he was happier (and cleaner) in my weeks and would I take him officially more often, like, er, all week? XH was given pretty much no choice in the matter, with social services hovering grimly in the background. Following a meeting at the school DS came home with me and seemed hugely relieved.
He's 13 now, still working through some of the issues, poor mite, but cheerful and secure for the most part. He sees his dad occasionally but does not express the wish to spend time in his company. XH has offered him treats like a day at the seaside which I said he is quite welcome to go on, but I think we both know that it isn't actually ever going to happen because days at the seaside are things that mummies organise.
Not sure where that gets you with your DD. It will inevitably be a shock to her and there's no telling where her loyalties may go initially. There's also no guarantee that her dad won't be putting his side of things when you aren't there, and let's face it, children are programmed to learn from their parents, so the one who gets the story in first is likely to be believed. Unfortunately the more unscrupulous parent wins this kind of one-way contest in the short term. I can only say that if you don't compromise your beliefs, if you continue to treat her with kindness and consideration, be truthful but not tactless, and of course always make it clear just how much you love her (without ever, ever trying to suggest you love her more than the other parent does, that is so no-win), she should accept before long that she has two parents but not together, and that she is not losing any love because of it. There does not have to be a "good" parent and a "bad" parent, just two people who don't make each other happy. Very best of luck with that, it isn't easy...