The vague outline I'm thinking of for my female Qunari is going to be a Qun-hating, snarky and cunning sellsword who loves her job and revels in the fact that she isn't a priest or a shopkeeper or whatever 'nonsense' the Qun would have had her doing if she grew up there rather than the south. She's pretty much neutral in most political affairs without any real conviction in anything, and would just side with whoever would be most beneficial for her Inquisition. She won't be entirely without conscience, but she'll take money over principle any day - unless it involves selling out her homies. You'd need to make a very good offer for that. Outwardly, she'll be rather likable, so she might get along alright with most.
So, from what we know of companions...
Iron Bull and her will probably hit it off just fine. Probably become merc homies.
Blackwall seems to be the noble, honorable type, so I imagine there will be some clashing ideals here and there.
Cassandra, same as above. But I think I'll probably figure out some way to get a mutual respect for both of them.
She might get along with Varric. They both like to talk, both like money...and while Varric is probably a more morally good person that she is, it's not like I plan to make her kick babies and burn down puppy shelters or anything. And what Varric always seemed to hate most was betraying friends, which isn't something she would really do. If he managed to become besties with sarcastic Hawke, he'll become besties with her.
Sera and her will probably have similar fun-loving personalities, but I imagine she would frown upon the fact that if there was a situation where Inquisitor had to choose between lowly peasants and nobles she'd probably choose nobles, just because they'd give her a heavier coin purse and more soldiers and the like.
Dorian...I don't know. I guess they might be cool with eachother, sometimes?
Same goes for Solas. I don't think I really have his moral code figured out.
She'll probably get on with Vivienne alright. Other than the fact that Vivienne seems to have some very heavy convictions while Inquisitor will have pretty much none.