Oh, I loved this choice.
You've got Loghain with you. In that circumstance, I would say no to Morrigan and throw Loghain at the dragon. So would my Dalish Elven Rogue, Senteril. There's a reason why I'm making a distinction between myself and my character though...
However, during my playthrough, it was Senteril or Alistair. Now, if I had been in the situation myself I would have still said no to Morrigan, and thrown myself on the Archdemon. The risk is just too big. For all we know, if the child encounters the darkspawn at some or other point, we could have another Blight on our hands.
But I chose to have Senteril say yes.
And I'm someone who always chooses I would do when playing RPGs. This is the one time that I didn't.
Part of this was metagaming. I wanted to be able to import Senteril into Awakening, and that required him to be alive. (You can import dead characters into Awakening, and they show up alive without any explanation. And then they return to being dead if you import that save to DA2. Bioware could have done that better, I feel...)
But I crafted an in-character explanation to why Senteril said yes. Mainly, he didn't want to die. He didn't want to leave Leliana behind. Yes, that's completely ignoring the Warden's duty, and it's exactly what Wynne warned might happen, but I like that aspect. It makes Senteril more interesting if he isn't quite perfect.
He also, despite everything, does trust Morrigan. And he is willing to spend the rest of his life to do as much as he can to stop his actions from triggering another Blight. Senteril made another... questionable... deal during Awakening, with the aim of achieving just that. I headcanon that Blightblood (the reward for playing the Darkspawn Chronicles DLC) is a weapon forged from the body of the Archdemon, which Senteril carries with him as a constant reminder of his own weakness.
This then leads to Witch Hunt, which aptly demonstrates unique friendship-despite-differences between Morrigan and Senteril. They are two people who trust each other. Morrigan has saved Senteril's life (although he regrets the choice) and he spends the entire DLC tracking her down just because she might be in danger. And that's purely out of friendship - something that Morrigan doesn't entirely understand, but appreciates nonetheless.
So yeah, all in all, I loved that choice because it was the opportunity for Senteril to show some serious character development.
I have done a playthrough where I threw Loghain at the Archdemon though, and that is a very satisfying ending. The Hero of River Dane earning his final redemption...