To be honest i find any non-human inquisitor to be a bit forced as the leader of the inquisition, which is an human organization (look at your advisors and your soldiers). Some adjustments were made in the plot since bioware announced the multiple races, but i remain unconvinced, i find the whole thing more believable (including the herald of andraste stuff) if you play as a human.
I am not saying that people cannot play as anything else, just stating my opinion that DAI story seems heavily focused on human stuff, and the other races feel rather tacked on for my tastes. I think DAO was better done in that regard because the wardens were established from the beginning to be multi-raced, even back then, some races felt better introduced than others (ex. lack of difference playing human vs elf).
I want to emphatise that this is my opinion, feel free to ignore it and enjoy your qunari herald of andraste. I however find it too unbelievable (like a hawke mage in DA2 who continually gets free pass as an apostate), so i would rather pick something that does not break my suspension of disbelief.