I'd go with something along the lines of Vivienne's "marriage is just a matter of titles and inheritance" line. He's more enamored with the person behind the title of Inquisitor than all of the baggage that comes with it.
Or he responds with "That is a horrible idea, we have to do it." because it would irk Halward to no end. A few weeks later the Inquisitor realizes that he's unleashed Groomzilla on an unsuspecting Skyhold.
The world needs Groomzilla Dorian. Immediately. If only to prove how impressive Josephine's diplomatic skills are.
I could definitely see him refusing out of principle, arguing that marriage does not equal love, or your bond is more important than a piece of paper or, more cynically, marriage hasn't been a joyful occasion for most of the people he knows. If he did accept, though, I'd imagine one of three scenarios:
1) The one mentioned above, where he thinks that Quizzy is joking, is struck speechless, and is then stunned but delighted.
2) Initially refusing, then mulling it over, realising that yes, actually, this just might be something he wants, then turning around and re-proposing to the Quizzy himself (if anyone's proposing, it'll be him: he does like to be in charge of some things, thank you very much, and he certainly has better taste in accessories like jewellery).
3) Blindsiding both the Quizzy and the player by squeeing happily and immediately agreeing just in case his fiance changes his mind; having to chase off every noble who thinks a marriage with the Inquisitor would be politically advantageous gets tiring after a while. Let's see them try to take on his legal spouse.
I would think the first one would be far more likely: the third would probably be done just to surprise the player, and the second sounds rather like another DA love interest (albeit without the marriage aspect).
Dorian: You know, usually this sort of thing would involve my lackeys kidnapping you in the night and delivering you to the throne room of my fancy mage tower. "Bathe him and bring him to my chambers!",maniacal laughter, all the classics.
That line should be put into the game. That is EXACTLY the kind of thing Dorian would say.