Gonna do multiple replies just 'cause. I am so new to the Bioware forums it's almost embarrassing 
The Qun would be good for the male dwarves, but not so much for the battle hard female dwarves. Most surface dwarves probably will stick to not believing in anything or take up their chances with the chantry, which I plan to explore on my first play-through. The glowing hand on a dwarf may influence some change in people mind. To be quite honest, I think the people are denying non-human as the herald, because they refuse to believe that the Maker's chosen could be only human.
Oh yeah, I forgot about the gender roles in the Qun. I can imagine them having an OK impression of the Chantry though. It's the dominant surfacer religion - even though the religion is probably better in theory than practice - and they'd probably encounter their fair share of templars and mages due to the lyrium trade. If nothing else, Andrastianism is good business for lyrium-smuggling dwarves.
First of all - Hi! Welcome to our Dwarven Family! 
I'm pretty sure some surfacers are Andrastians - if City Elves can do it - then dwarves shouldn't be worse. And surfacers are more tolerant then Orzammar's crawd. My Merry will be an Adrastian.
As for Qun - I guess it's possible for dwarves to convert to Qun. However, I think it's more Elf thing. Also as Cespar said I very much doubt brave female dwarves would like Qun.
Tell us more about Tashra Cadash. Do you have her all planned out? 
Hi and thanks for the welcome!
Merry sounds adorable!
I'm leaning towards making Tashra an Andrastian as well. She's a practical Carta girl who loves the surface. She's a smuggler by trade, and uses her network to get herself all the new toys (grenades, darts, poisons, jars of bees...), and has a bad impression of elves because of an encounter with my Lavellan. Templar sympathetic because of encounters of lyrium addicts.
Thinking about Daggers/Tempest or Daggers/Artificer.
Its good to see our Dwarven family continue to grow I am planning on my first PT will be a Male Dwarf Greatsword wielding Warrior/Champion and I intend to model him off of Kaiden from ME 1.
since we don't have Varric will the handsome Kaidan dwarf be romanceable I mean, he sounds like an excellent fellow.