For a non-mage who drinks, I think it would be compelling to consider the religious implications of it. He does take his religion very seriously and if your quizzie does as well...I could imagine some really interesting dialouge where he questions her on this. How would a non-mage Andrastian defend herself on this decision? Would he be more concerned about what could happen to her or more concerned about why she would make a decision like this? Cullen is pretty laid back, but he gets pretty stressed over the quizzie's choice to become a templar. This seems at least as big as that, because now she is bound to some old god. i can't imagine he would take it well.
I did this on my human rogue PT. I'm having a hard time headcanoning without seeing how Bioware deals with it in a DLC (and I really hope they do), so I'm kind of useless. I think on the inside he's probably freaking out but trying to stay calm and hoping for the best. I did it because the knowledge from the Well needed to stay with the Inquisitor and I explained that to him and he understood, but really didn't like it. I'd also gone in, as the Inquisitor, assuming that Solas would stay and help me understand, but naturally he didn't. (Although, as the player, I already knew by then that he wouldn't be staying.) So, yeah, I honestly don't know.
Hmmmm.... this is all very interesting stuff to think about. Yes, my main block is that, as a non-mage, this is all very new and confusing, something she has no experience with and he has in plenty - on top of it being religiously complicated to reconcile all these notions of the Maker guiding her hand with surrendering herself to an elven god. At heart, my IQ made this choice in this playthrough because she didn't trust Morrigan, but even that only goes so far once it's done and she has to live with the consequences and implications of it. I'll have to find my original playthrough and do this over in that one because this one has Kieran alive and I just found out the scene with Flemeth plays out completely different if he exists, so that doesn't help me much with my canon, but I did get a good part where Quizzie is puppeteered by Flemeth and that added a ton of weight to the choice too. It's a really interesting path for the Inquisitor to take, but it comes with a lot of thorns of its own.
Well, you've all given me much to think about, and that's what I wanted, so thank you guys! 