It never ceases to amaze me that because a parent loves someone the assumption is that their children should automatically love them as well. Not only that, but that they should embrace them as a parental figure.
OP, it concerns me that you have sold this man to your DD as a potential father figure hence the comments about her wanting her real dad. Why else would she be lashing out saying she wanted her real dad and not him?
I don't think that a child should be able to dictate whether a parent has relationships but I do think that there is middle ground between a parent just embracing the whole relationship with the expectation that the children need to suck it up. If a child is telling you that they don't like your partner or your relationship then you need to talk this through with them and establish the reasons behind it. And it's not always going to be just about jealousy, it may be that they genuinely don't like them, or the way in which they're expected to relate to them, and actually, they're entitled to those feelings, whether we as parents like it or not.
The fact is that this man is not even remotely in a place to be acting as a father figure to your DD yet. You've been in the relationship for eight months, even you can't be sure that it will last as you're still in the honeymoon phase. You need to step way, way back in terms of the expectations of the relationship between this man and your DD and your expectations of her. And while she needs to be polite and considerate, you need to also talk to her about what she's feeling and why.
Also, is it really true that her dad is shit? Or is it that you got pregnant during a casual relationship and he didn't want the baby while you were pregnant, he moved abroad and once she was born he has embraced her, but because he lives abroad that relationship is automatically going to be more sporadic? Be careful to write someone off based on their reaction to a pregnancy announcement. Bearing in mind many women post here saying they're considering termination when they find themselves unexpectedly pregnant, who then go on to have the baby anyway. Nobody judges them for not wanting the baby at pregnancy stage.
You can never, ever tell her what you think of her dad. Because actually, her relationship with him is separate from yours, and even if you despise him, he is a good dad in her head and whether this is true or not she has to come to that realisation herself. And it's possible that there relationship will be positive, and again, you cannot control that based on your own feelings towards him. Added to that, if you were to express your feelings towards him this will just drive your DD further away from you.