Not allowing a older child privacy and pretty much confining them (as face it that's what you would have to do to to prevent one whose very determined) would be likely to be and could very easily meet the significant harm bar.
12 isn't an older child though, the law doesn't even see them as an older child as demonstrated by consent laws. An older child is 15+.
If my child was hellbent on having sex, I'd be hellbent on stopping them. Even if it meant putting her in an all girls boarding school where she'd be getting strict supervision from teachers who's full time job was to watch them. Just like if she was on drugs I'd be forcing her into a rehab center where she'd be under strict supervision to stop it.
Considering that you as the parent will be footing the bill to raise a second baby at that age, I think it's quite reasonable to crack down. Not to mention there are serious and permanent health risks to having a baby or even an abortion at so young. A pregnant child could very well die or have serious complications. I think that's worth going to the ends of the earth to prevent.
Privacy does not mean no supervision or even being allowed to hang out with friends where no adult is present. It means they have the right to use the bathroom with the doors closed and get dressed without anyone watching. That's it.
If she doesn't have the responsibility to handle anymore freedom than that, then that's all the freedom she'd get until she could prove otherwise. As she demonstrated that she was more mature and could be trusted more, I'd give her privileges back. I wouldn't be harping on what a terrible and shameful daughter she was every night. But I would be actively involved in getting her life turned around, even if that meant talking to teachers to make sure she was attending classes.
Frankly, I'd rather my child feel hard done by and "abused" than having to live with a terrible consequence from her childish decisions the rest of her life. Hopefully as she got older, she'd see that my restrictions came from a place of love.
But she certainly wouldn't be thanking me for just letting her get pregnant or hooked on drugs. In fact I can't think of a single person who as an adult has thanked their parents for letting them run amok and get into trouble. Most wished their parents cared enough to stop them.