I agree with other posters, OP, in that I think you're rushing into this "she needs to know her half-sibling!!!" without necessarily understanding the potential harm that this entire mess will do to your DD. However, I also understand your ex's reluctance to tell your DD that he's not her biological father. He's frightened of losing her, I suspect, even though he has proven himself to be her Dad, simply by dint of his being there even after your split.
What will you do when she asks to meet her biological father? Because... chances are that she will. And, as her mother, you'll have to deal with that as appropriately as you can. Especially given the circumstances as to why he's not been in her life...
My father is the oldest of 8 children. 3 from one relationship, 4 from another, and 1 from the very last. His parents split wasn't my grandfather's fault, but he disappeared from my father and uncles lives completely. My father was just a year older than your DD is now... and he never saw his biological father again. We all knew about there being half-siblings - because my grandmother told us about them. She and my grandfather, seemingly, kept in touch through the years... but there was no contact for any of his oldest children, not whilst they were being raised by someone else. Shortly before my grandmother's partner's death, I tracked my half-aunt and uncles down - because I was curious. The ramifications of doing that were horrendous. My grandmother's partner died, never having forgiven me for rejecting her as a grandparent (which I didn't - I simply wanted to know where I came from, so that I could tell my own children where they came from, too. But I have to live with that guilt for the rest of my life.). My grandfather had died and no one had thought to tell his oldest three children, so there was that heartbreak to deal with... and then they all decided that they needed to know their half-siblings. My two uncles met them, were rude and nasty, and refused to have anything else to do with them after that - which confused their younger half-siblings, who were also the innocent parties. They'd known about their older brothers, but not how to find them (I tracked down a cousin via a family tree site). My father met them, made a half-hearted attempt at a relationship with them, but after a year or so, decided that they were "all drunks" and/or "weird" (my half-aunt is religious). So he dropped them, too. Their names cannot be mentioned at all. Meanwhile, the oldest of the sons of the next 4, got his knickers spectactularly in a knot because even though he'd always known he wasn't my grandfather's eldest son... suddenly the eldest son was physically present in their lives. It's taken years for him to climb down off his high horse about that - even though it didn't actually affect him one way or the other. He's still his younger full siblings oldest brother, after all.
On the plus side, my children and I have relationships with them all - except the youngest aunt, who is three years my junior and can't cope with having us in her life. She doesn't talk to any of her older siblings. That's her perogative. One day we hope she'll change her mind. I have a pretty good relationship with my two oldest half-cousins, who were able to tell me what our grandfather was like. My daughter and son are close with my youngest half-cousins, because they're the same ages. Luckily, for us, it's worked out. But it so easily might not have...
Meanwhile, my DD (20) has a biological father and a dad. Two separate men. She's never - to the best of my knowledge - met her biological father (he was abusive to me and I ran), although she had a relationship with her paternal biological grandparents and their other children until she was 7 years old, and decided she'd had enough. I don't know why. She won't tell me/claims she doesn't remember. But she always knew they were her biological family. A few years later, I split from the man who had always been dad to her. He has a relationship with our DS (11), but not with DD. Again, that was her choice... but it broke my heart, time and time again when she'd refuse to spend time with him, but cried because DS was off "having fun with daddy" and she wasn't. DS sees his half-siblings as regularly as I can arrange it. DD last saw them when the oldest was a baby (she's 7 now). She also has three biological half-siblings from her biological father... whom she's never met. She doesn't want to. At all. I suspect that, if they find out about her, they'll come looking - and she'll reject them. Which will hurt. Her, as well as them.
What I'm trying to say, OP, is that not everything has a happy ending. We can hope for and try to achieve one... especially when it comes to our children, but it's not always possible. My honest advice would be not to rush into something that will have a profound affect upon your DD. She might not react now, but she will at some point. Yes, she needs to know that her daddy isn't biologically related to her (and yes; you should have told her this from the get-go), but she also doesn't need a half-sibling physically thrown into her life in the same time frame. Discovering that her daddy isn't... that's going to be confusing enough, and your ex needs to be aware that she'll possibly be quite angry at you both for a while. He needs to really step up and reassure her that he loves her, and he's not going anywhere... and so do you.
