I understand she was "promoted" but didn't Riot mention that she didn't fit in? Well visually speaking she fits right in with the Demacian elite.

You can "not fit in" in more ways than only in visual one.

She doesn't fit in with her mannerisms and self-evaluation, she just looks like an elite.

I'm just hoping they can make a skin for her from before her big promotion.

To play devil's advocate, and I say this as someone who agrees with you, we really have no idea how much time has passed between her acceptance into the upper echelons of the Demacian military and her arrival at the League. For all we know, she could've spent a year or more in service to the Vanguard before achieving sufficient renown to be put considered a suitable candidate.

I'd like to think she wasn't just fast-tracked to the Institute and handed a gaudy set of bird-themed armour as a going-away present.

Look beneath the armor and poise to see what is beneath. I've been to parties and gatherings where I was dressed the same as everyone else, but since I was a stranger, I didn't look like I fit in, and certainly didn't feel like it. Quinn's role is different than other Demacian champs so far (their first true 'counter assassin'), and her social upbringing doesn't help. She's got the skills, but not the nobility.